1. Discuss how the establishment of an organizational infrastructure that supports the integration of a career and succession plan competency models and value systems can help employees overcome the doom loop with respect to understanding your own career status.

1. Discuss how the establishment of an organizational infrastructure that supports the integration of a career and succession plan competency models and value systems can help employees overcome the doom loop with respect to understanding your own career status.

A number of associations or organizations are mixing up to … Read More...
2. The failure density distribution for mechanical component is given by: fT(t) = (ct)* exp(-.5*c*t^2) where ‘c’ is a parameter of the distribution. Determine: • Cumulative distribution of the failures (5 points) • Reliability of the components (5 points) • Hazard rate for the components (5 points) • Mean, standard deviation of the failure distribution and reliability of components at the end of 2 years, when c=0.0025 (5 points) • Plot the Failure rate density function, Failure time distribution function, Reliability function and Hard Rate function for the given distribution when c=0.0025 (5 points)

2. The failure density distribution for mechanical component is given by: fT(t) = (ct)* exp(-.5*c*t^2) where ‘c’ is a parameter of the distribution. Determine: • Cumulative distribution of the failures (5 points) • Reliability of the components (5 points) • Hazard rate for the components (5 points) • Mean, standard deviation of the failure distribution and reliability of components at the end of 2 years, when c=0.0025 (5 points) • Plot the Failure rate density function, Failure time distribution function, Reliability function and Hard Rate function for the given distribution when c=0.0025 (5 points)

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The next two questions refer to this situation: A rectangular loop with sides of length a= 1.50 cm and b= 4.00 cm is placed near a wire that carries a current that varies as a function of time: i(t)=3.90+1.22t2 where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d= 0.350 centimeters. What is the magnetic flux through the loop at time t= 0.80 seconds? (Define positive flux into the page.)

The next two questions refer to this situation: A rectangular loop with sides of length a= 1.50 cm and b= 4.00 cm is placed near a wire that carries a current that varies as a function of time: i(t)=3.90+1.22t2 where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d= 0.350 centimeters. What is the magnetic flux through the loop at time t= 0.80 seconds? (Define positive flux into the page.)

 
1. (20 pts) The linear momentum operator in one dimension is given by: ˆpx = ! i d dx . In class we said that the average momentum for a particle in a box (pib) is 0. Use the formula for the expectation value to verify mathematically that this is true. The pib-wavefunction: 2 ℓ sin nπ ℓ x ! ” # $ % & 2. (20 pts) Evaluate the following commutators: a. (10 pts) b. (10 pts) 3. (20 pts) A certain one-dimensional quantum mechanical system is described by the Hamiltonian: , q is a constant, and 0 ≤ x ≤ ∞. One of the eigenfunctions is known to be: a. (15 pts) Find the value of N to normalize the function. b. (5 pts) By letting , find the energy eigenvalue. 4. (20 pts) The Schrödinger equation for the particle on a sphere (a.k.a. the Rigid Rotor) is: − !2 2μR2 1 sinθ ∂ ∂θ sinθ ∂ ∂θ # $ % & ‘ ( + 1 sin2θ ∂2 ∂φ 2 # $ % & ‘ ( ψ(θ,φ ) = Eψ(θ,φ ) A purported eigenfunction for it is: ψ(θ,φ ) = N sin3θ cos(3φ ) a. (15 pts) Use this wave function to find the energy eigenvalue for the function. (You do NOT have to normalize the function!). b. (5 pts) The eigenvalues for the particle on a sphere are of the form: Eℓ = “2 2μR2 ℓ(ℓ +1) What is the value of ℓ for the wave function used in part a? 5. (20 pts) Using the ortho-normailty of the hydrogenic orbitals and the spin functions, normalize the excited Helium atom represented by the following wave function: ψ = N 1s({ 1)2p(2)+ 2p(1)1s(2)}{α(1)β (2)−β (1)α(2)} ˆ x, ( ˆpx [ + xˆ)] = ˆpx, ( ˆ x)3 !” #$ = ˆH = − 2 2m d2 dx2 − q2 x ψ(x) = Nxe−α x α = mq2 / 2

1. (20 pts) The linear momentum operator in one dimension is given by: ˆpx = ! i d dx . In class we said that the average momentum for a particle in a box (pib) is 0. Use the formula for the expectation value to verify mathematically that this is true. The pib-wavefunction: 2 ℓ sin nπ ℓ x ! ” # $ % & 2. (20 pts) Evaluate the following commutators: a. (10 pts) b. (10 pts) 3. (20 pts) A certain one-dimensional quantum mechanical system is described by the Hamiltonian: , q is a constant, and 0 ≤ x ≤ ∞. One of the eigenfunctions is known to be: a. (15 pts) Find the value of N to normalize the function. b. (5 pts) By letting , find the energy eigenvalue. 4. (20 pts) The Schrödinger equation for the particle on a sphere (a.k.a. the Rigid Rotor) is: − !2 2μR2 1 sinθ ∂ ∂θ sinθ ∂ ∂θ # $ % & ‘ ( + 1 sin2θ ∂2 ∂φ 2 # $ % & ‘ ( ψ(θ,φ ) = Eψ(θ,φ ) A purported eigenfunction for it is: ψ(θ,φ ) = N sin3θ cos(3φ ) a. (15 pts) Use this wave function to find the energy eigenvalue for the function. (You do NOT have to normalize the function!). b. (5 pts) The eigenvalues for the particle on a sphere are of the form: Eℓ = “2 2μR2 ℓ(ℓ +1) What is the value of ℓ for the wave function used in part a? 5. (20 pts) Using the ortho-normailty of the hydrogenic orbitals and the spin functions, normalize the excited Helium atom represented by the following wave function: ψ = N 1s({ 1)2p(2)+ 2p(1)1s(2)}{α(1)β (2)−β (1)α(2)} ˆ x, ( ˆpx [ + xˆ)] = ˆpx, ( ˆ x)3 !” #$ = ˆH = − 2 2m d2 dx2 − q2 x ψ(x) = Nxe−α x α = mq2 / 2

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Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

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MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis MAE 318: System Dynamics and Control Homework 4 Problem 1: (Points: 25) The circuit shown in Fig. 1 is excited by an impulse of 0.015V. Assuming the capacitor is initially discharged, obtain an analytic expression of vO (t), and make a Matlab program that plots the system response to the impulse. Figure 1 Problem 2: Extra Credit (Points: 25) A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Fig. 2. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. Make a Matlab script that computes the system response and determine how long will it take until the motion decays to a swing of only 10 degrees? Assume that the thin wire has a rotational spring constant of 2  10?4Nm/rad and that the viscous friction coecient for the sphere in air is 2  10?4Nms/rad. Each sphere has a mass of 1Kg. Figure 2: Winding oscillator. Problem 3: (Points: 25) Find the equivalent transfer function T (s) = C(s) R(s) for the system shown in Fig. 3. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 1 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 3 Problem 4: (Points: 25) Reduce the block diagram shown in Fig. 4 to a single transfer function T (s) = C(s) R(s) . Figure 4 Problem 5: (Points: 25) Consider the rotational mechanical system shown in Fig. 5. Represent the system as a block diagram. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 2 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 5 Problem 6: (Points: 25) During ascent the space shuttle is steered by commands generated by the computer’s guidance calcu- lations. These commands are in the form of vehicle attitude, attitude rates, and attitude accelerations obtained through measurements made by the vehicle’s inertial measuring unit, rate gyro assembly, and accelerometer assembly, respectively. The ascent digital autopilot uses the errors between the actual and commanded attitude, rates, and accelerations to gimbal the space shuttle main engines (called thrust vectoring) and the solid rocket boosters to a ect the desired vehicle attitude. The space shut- tle’s attitude control system employs the same method in the pitch, roll, and yaw control systems. A simpli ed model of the pitch control system is shown in Fig. 6.  a) Find the closed-loop transfer function relating the actual pitch to commanded pitch. Assume all other inputs are zero.  b) Find the closed-loop transfer function relating the actual pitch rate to commanded pitch rate. Assume all other inputs are zero.  c) Find the closed-loop transfer function relating the actual pitch acceleration to commanded pitch acceleration. Assume all other inputs are zero. Figure 6: Space shuttle pitch control system (simpli ed). Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 3 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Problem 7: (Extra Credit Points: 25) Extenders are robot manipulators that extend (i.e. increase) the strength of the human arm in load- maneuvering tasks (see Fig. 7). The system is represented by the transfer function Y (s) U(s) = G(s) = 30 s2+4s+3 where U (s) is the force of the human hand applied to the robot manipulator, and Y (s) is the force of the robot manipulator applied to the load. Assuming that the force of the human hand that is applied is given by u (t) = 5 sin (!t), create a MATLAB code that will compute and plot the di erence in magnitude and phase between the applied human force and the force of the robot manipulator applied to the load, as a function of the frequency !. Use 100 values for ! in the range ! 2 [0:01; 100] rad s for your two plots. See Fig. 8 on how to de ne di erence in magnitude and phase between two signals. You need to include your code and the two resulted plots in your solution. Figure 7: Human extender. A B dt T: signal period magnitude difference phase difference B A Figure 8: Magnitude and phase di erence (deg) between two sinusoidal signals.

MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis MAE 318: System Dynamics and Control Homework 4 Problem 1: (Points: 25) The circuit shown in Fig. 1 is excited by an impulse of 0.015V. Assuming the capacitor is initially discharged, obtain an analytic expression of vO (t), and make a Matlab program that plots the system response to the impulse. Figure 1 Problem 2: Extra Credit (Points: 25) A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Fig. 2. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. Make a Matlab script that computes the system response and determine how long will it take until the motion decays to a swing of only 10 degrees? Assume that the thin wire has a rotational spring constant of 2  10?4Nm/rad and that the viscous friction coecient for the sphere in air is 2  10?4Nms/rad. Each sphere has a mass of 1Kg. Figure 2: Winding oscillator. Problem 3: (Points: 25) Find the equivalent transfer function T (s) = C(s) R(s) for the system shown in Fig. 3. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 1 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 3 Problem 4: (Points: 25) Reduce the block diagram shown in Fig. 4 to a single transfer function T (s) = C(s) R(s) . Figure 4 Problem 5: (Points: 25) Consider the rotational mechanical system shown in Fig. 5. Represent the system as a block diagram. Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 2 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Figure 5 Problem 6: (Points: 25) During ascent the space shuttle is steered by commands generated by the computer’s guidance calcu- lations. These commands are in the form of vehicle attitude, attitude rates, and attitude accelerations obtained through measurements made by the vehicle’s inertial measuring unit, rate gyro assembly, and accelerometer assembly, respectively. The ascent digital autopilot uses the errors between the actual and commanded attitude, rates, and accelerations to gimbal the space shuttle main engines (called thrust vectoring) and the solid rocket boosters to a ect the desired vehicle attitude. The space shut- tle’s attitude control system employs the same method in the pitch, roll, and yaw control systems. A simpli ed model of the pitch control system is shown in Fig. 6.  a) Find the closed-loop transfer function relating the actual pitch to commanded pitch. Assume all other inputs are zero.  b) Find the closed-loop transfer function relating the actual pitch rate to commanded pitch rate. Assume all other inputs are zero.  c) Find the closed-loop transfer function relating the actual pitch acceleration to commanded pitch acceleration. Assume all other inputs are zero. Figure 6: Space shuttle pitch control system (simpli ed). Arizona State University. Fall 2015. Class # 73024. MAE 318. Homework 4: Page 3 of 4 MAE 318: System Dynamics and Control Dr. Panagiotis K. Artemiadis Problem 7: (Extra Credit Points: 25) Extenders are robot manipulators that extend (i.e. increase) the strength of the human arm in load- maneuvering tasks (see Fig. 7). The system is represented by the transfer function Y (s) U(s) = G(s) = 30 s2+4s+3 where U (s) is the force of the human hand applied to the robot manipulator, and Y (s) is the force of the robot manipulator applied to the load. Assuming that the force of the human hand that is applied is given by u (t) = 5 sin (!t), create a MATLAB code that will compute and plot the di erence in magnitude and phase between the applied human force and the force of the robot manipulator applied to the load, as a function of the frequency !. Use 100 values for ! in the range ! 2 [0:01; 100] rad s for your two plots. See Fig. 8 on how to de ne di erence in magnitude and phase between two signals. You need to include your code and the two resulted plots in your solution. Figure 7: Human extender. A B dt T: signal period magnitude difference phase difference B A Figure 8: Magnitude and phase di erence (deg) between two sinusoidal signals.

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Programming Assignment 7: Poker (5-Card Draw) II. Prerequisites: Before starting this programming assignment, participants should be able to: Apply and implement pointers in C Pass output parameters to functions Analyze a basic set of requirements and apply top-down design principles for a problem Apply repetition structures within an algorithm Construct while (), for (), or do-while () loops in C Compose C programs consisting of sequential, conditional, and iterative statements Eliminate redundancy within a program by applying loops and functions Create structure charts for a given problem Open and close files Read, write to, and update files Manipulate file handles Apply standard library functions: fopen (), fclose (), fscanf (), and fprintf () Apply and implement pointers 2-dimenional arrays Define and apply structs in C Compose decision statements (“if” conditional statements) Create and utilize compound conditions Summarize topics from Hanly & Koffman Chapter 8 including: What is an array? Distinguishing between single dimensional and 2-dimentional arrays What is an index? III. Overview & Requirements: Write a program that allows a user to play 5-Card-Draw Poker against the computer. Start with the following example code supplied by Deitel & Deitel (example code). This will help you get started with the game of Poker. Please read this site to learn the rules of Poker http://en.wikipedia.org/wiki/5_card_draw. Complete the following step and you will have a working Poker game!!! Adapted from Deitel & Deitel’s C How to Program (6th Edition): (1) In order to complete the game of 5-card-draw poker, you should complete the following functions: (a) (5 pts) Modify the card dealing function provided in the example code so that a five-card poker hand is dealt. (b) (5 pts) Write a function to determine if the hand contains a pair. (c) (5 pts) Write a function to determine if the hand contains two pairs. (d) (5 pts) Write a function to determine if the hand contains three of a kind (e.g. three jacks). (e) (5 pts) Write a function to determine if the hand contains four of a kind (e.g. four aces). (f) (5 pts) Write a function to determine if the hand contains a flush (i.e. all five cards of the same suit). (g) (5 pts) Write a function to determine if the hand contains a straight (i.e. five cards of consecutive face values). (2) (20 pts) Use the functions developed in (1) to deal two five-card poker hands, evaluate each hand, and determine which is the better hand. (3) (25 pts) Simulate the dealer. The dealer’s five-card hand is dealt “face down” so the player cannot see it. The program should then evaluate the dealer’s hand, and based on the quality of the hand, the dealer should draw one, two, or three more cards to replace the corresponding number of unneeded cards in the original hand. The program should then re-evaluate the dealer’s hand. (4) (10 pts) Make the program handle the dealer’s five-card hand automatically. The player should be allowed to decide which cards of the player’s hand to replace. The program should then evaluate both hands and determine who wins. Now use the program to play 10 games against the computer. You should be able to test and modify or refine your Poker game based on these results!

Programming Assignment 7: Poker (5-Card Draw) II. Prerequisites: Before starting this programming assignment, participants should be able to: Apply and implement pointers in C Pass output parameters to functions Analyze a basic set of requirements and apply top-down design principles for a problem Apply repetition structures within an algorithm Construct while (), for (), or do-while () loops in C Compose C programs consisting of sequential, conditional, and iterative statements Eliminate redundancy within a program by applying loops and functions Create structure charts for a given problem Open and close files Read, write to, and update files Manipulate file handles Apply standard library functions: fopen (), fclose (), fscanf (), and fprintf () Apply and implement pointers 2-dimenional arrays Define and apply structs in C Compose decision statements (“if” conditional statements) Create and utilize compound conditions Summarize topics from Hanly & Koffman Chapter 8 including: What is an array? Distinguishing between single dimensional and 2-dimentional arrays What is an index? III. Overview & Requirements: Write a program that allows a user to play 5-Card-Draw Poker against the computer. Start with the following example code supplied by Deitel & Deitel (example code). This will help you get started with the game of Poker. Please read this site to learn the rules of Poker http://en.wikipedia.org/wiki/5_card_draw. Complete the following step and you will have a working Poker game!!! Adapted from Deitel & Deitel’s C How to Program (6th Edition): (1) In order to complete the game of 5-card-draw poker, you should complete the following functions: (a) (5 pts) Modify the card dealing function provided in the example code so that a five-card poker hand is dealt. (b) (5 pts) Write a function to determine if the hand contains a pair. (c) (5 pts) Write a function to determine if the hand contains two pairs. (d) (5 pts) Write a function to determine if the hand contains three of a kind (e.g. three jacks). (e) (5 pts) Write a function to determine if the hand contains four of a kind (e.g. four aces). (f) (5 pts) Write a function to determine if the hand contains a flush (i.e. all five cards of the same suit). (g) (5 pts) Write a function to determine if the hand contains a straight (i.e. five cards of consecutive face values). (2) (20 pts) Use the functions developed in (1) to deal two five-card poker hands, evaluate each hand, and determine which is the better hand. (3) (25 pts) Simulate the dealer. The dealer’s five-card hand is dealt “face down” so the player cannot see it. The program should then evaluate the dealer’s hand, and based on the quality of the hand, the dealer should draw one, two, or three more cards to replace the corresponding number of unneeded cards in the original hand. The program should then re-evaluate the dealer’s hand. (4) (10 pts) Make the program handle the dealer’s five-card hand automatically. The player should be allowed to decide which cards of the player’s hand to replace. The program should then evaluate both hands and determine who wins. Now use the program to play 10 games against the computer. You should be able to test and modify or refine your Poker game based on these results!

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There is a term called “hydrotherapy” (http://en.wikipedia.org/wiki/Hydrotherapy), which states that cold water bath can reduce pain and improve health, especially immune function. Explain the possible benefits and possible problems of hydrotherapy with the information you learned.

There is a term called “hydrotherapy” (http://en.wikipedia.org/wiki/Hydrotherapy), which states that cold water bath can reduce pain and improve health, especially immune function. Explain the possible benefits and possible problems of hydrotherapy with the information you learned.

Hydrotherapy is the use of water to treat a disease … Read More...