Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wing B and C are located as shown.

## Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wing B and C are located as shown.

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The Rocket Equation The Tsiolovsky Rocket Equation describes the velocity that results from pushing matter (exploding rocket fuel) in the opposite direction to the direction you want to travel. This assignment requires you to do basic calculation using the Tsiolovsky Rocket Equation : v[t] = eV Log M M – bR t  – g t The parameters used are : ◼ eV exhaust velocity (m/s) ◼ pL payload (kg) ◼ fL fuel load (kg) ◼ M is the mass of the rocket (pL+fL, kg) ◼ bR the burn rate of fuel (kg/s) ◼ g the force due to gravity ms2 The variables calculated are : h(t) the height of the rocket at time t (m) v(t) the velocity of the rocket at time t (m/s) m(t) the mass of the rocket at time t (kg) Questions Question 1 (1 mark) Write an expression corresponding to the Tsiolovsky rocket equation and use integrate to find a function to describe the height of the rocket during fuel burn. Question 2 (2 marks) The fuel burns at a constant rate. Find the time (t0), velocity (vmax), and height (h0) of the rocket when the fuel runs out (calculate the time when the fuel runs out, and substitute this into the height Printed by Wolfram Mathematica Student Edition and velocity equations). Question 3 (2 marks) The second phase is when the only accelaration acting on the rocket is from gravity. This phase starts from the height and velocity of the previous question, and the velocity is given by the projectile motion equation, v(t) = vmax – g (t – t0). Use Solve to find the time when this equation equals 0. This will be the highest point the rocket reaches before returning to earth. Question 4 (1 marks) Integerate the projectile motion equation and add h0 to find the maximum height the rocket reaches. Question 5 (1 marks) Use Solve over the projectile motion equation to find the time when the height is 0. 2 assignment4.nb Printed by Wolfram Mathematica Student Edition

## The Rocket Equation The Tsiolovsky Rocket Equation describes the velocity that results from pushing matter (exploding rocket fuel) in the opposite direction to the direction you want to travel. This assignment requires you to do basic calculation using the Tsiolovsky Rocket Equation : v[t] = eV Log M M – bR t  – g t The parameters used are : ◼ eV exhaust velocity (m/s) ◼ pL payload (kg) ◼ fL fuel load (kg) ◼ M is the mass of the rocket (pL+fL, kg) ◼ bR the burn rate of fuel (kg/s) ◼ g the force due to gravity ms2 The variables calculated are : h(t) the height of the rocket at time t (m) v(t) the velocity of the rocket at time t (m/s) m(t) the mass of the rocket at time t (kg) Questions Question 1 (1 mark) Write an expression corresponding to the Tsiolovsky rocket equation and use integrate to find a function to describe the height of the rocket during fuel burn. Question 2 (2 marks) The fuel burns at a constant rate. Find the time (t0), velocity (vmax), and height (h0) of the rocket when the fuel runs out (calculate the time when the fuel runs out, and substitute this into the height Printed by Wolfram Mathematica Student Edition and velocity equations). Question 3 (2 marks) The second phase is when the only accelaration acting on the rocket is from gravity. This phase starts from the height and velocity of the previous question, and the velocity is given by the projectile motion equation, v(t) = vmax – g (t – t0). Use Solve to find the time when this equation equals 0. This will be the highest point the rocket reaches before returning to earth. Question 4 (1 marks) Integerate the projectile motion equation and add h0 to find the maximum height the rocket reaches. Question 5 (1 marks) Use Solve over the projectile motion equation to find the time when the height is 0. 2 assignment4.nb Printed by Wolfram Mathematica Student Edition

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In case the body have to stay in lower temperature for extended time period (more than 1 hour), how does the body regulate its response?

## In case the body have to stay in lower temperature for extended time period (more than 1 hour), how does the body regulate its response?

Arterioles transporting blood to external capillaries beneath the surface of … Read More...

F7.10 The flame spread rate through porous solids increases with … Read More...
Transportation 1. What would be some major benefits to a city investing in mass transit? • Reduces congestion and fuel usage o 2011 – U.S. public transportation use saved 865 million hours in travel time and 450 million gallons of fuel in 498 urban areas o Decrease the need for road enhancements o Can be quicker to get to work when roads are congested o Incentivizes exercise o Mass transit can have less land use requirements • Provides economic opportunities o revitalization of cities o Provides jobs in transportation o City makes money off of transit revenue o More appealing to tourists • Air quality o Cuts carbon emissions by 37 million metric tons annually o Air quality improvement for the city (less smog) • Safety o Reduce the number of accidents 2. What would be some major benefits to the users of mass transit? • Traffic o Reduces frustration of driving in traffic o Reduces the need for gas in traffic o Reliable and predictable time of arrival o More options to travel o No waiting in DMV lines • Economics o Public transit vs. owning, driving, and parking a car = \$803/month average savings (~\$10,000 a year) o Connects people who don’t have a car to jobs, healthcare, home o Provides jobs in transportation o No longer have to pay car insurance • Social o Can interact/meet new people every day o Connects communities o Can do other things, like read, on the train or bus o Reduce in stress o • Safety o Reduce risk of accidents

## Transportation 1. What would be some major benefits to a city investing in mass transit? • Reduces congestion and fuel usage o 2011 – U.S. public transportation use saved 865 million hours in travel time and 450 million gallons of fuel in 498 urban areas o Decrease the need for road enhancements o Can be quicker to get to work when roads are congested o Incentivizes exercise o Mass transit can have less land use requirements • Provides economic opportunities o revitalization of cities o Provides jobs in transportation o City makes money off of transit revenue o More appealing to tourists • Air quality o Cuts carbon emissions by 37 million metric tons annually o Air quality improvement for the city (less smog) • Safety o Reduce the number of accidents 2. What would be some major benefits to the users of mass transit? • Traffic o Reduces frustration of driving in traffic o Reduces the need for gas in traffic o Reliable and predictable time of arrival o More options to travel o No waiting in DMV lines • Economics o Public transit vs. owning, driving, and parking a car = \$803/month average savings (~\$10,000 a year) o Connects people who don’t have a car to jobs, healthcare, home o Provides jobs in transportation o No longer have to pay car insurance • Social o Can interact/meet new people every day o Connects communities o Can do other things, like read, on the train or bus o Reduce in stress o • Safety o Reduce risk of accidents

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F6.1 Piloted ignition occurs when the lower flammable limit is reached in the gas phase in the vicinity of the ignition pilot. True False F6.2 The flashpoint of a liquid fuel is always lower than its boiling point. True False F6.3 The vapor concentration just above the surface of a boiling liquid is 100%. True False F6.4 The autoignition temperature of a liquid fuel is close to its boiling point. True False F6.5 Piloted ignition of solid fuels typically occurs at surface temperatures ranging from 250°C to 400°C, while autoignition temperatures usually exceed 500°C. True False F6.6 Except for very low heating conditions, the physical thickness of objects that exhibit “thin” piloted ignition behavior is typically of the order of 0.1-0.2 mm. 1-2 mm. 10-20 mm. F6.7 The time to piloted ignition of a “thin” object is proportional to the inverse of the net heat flux at its exposed surface. True False F6.8 The time to piloted ignition of a “thick” object is proportional to the inverse of the net heat flux at its exposed surface. True False

## F6.1 Piloted ignition occurs when the lower flammable limit is reached in the gas phase in the vicinity of the ignition pilot. True False F6.2 The flashpoint of a liquid fuel is always lower than its boiling point. True False F6.3 The vapor concentration just above the surface of a boiling liquid is 100%. True False F6.4 The autoignition temperature of a liquid fuel is close to its boiling point. True False F6.5 Piloted ignition of solid fuels typically occurs at surface temperatures ranging from 250°C to 400°C, while autoignition temperatures usually exceed 500°C. True False F6.6 Except for very low heating conditions, the physical thickness of objects that exhibit “thin” piloted ignition behavior is typically of the order of 0.1-0.2 mm. 1-2 mm. 10-20 mm. F6.7 The time to piloted ignition of a “thin” object is proportional to the inverse of the net heat flux at its exposed surface. True False F6.8 The time to piloted ignition of a “thick” object is proportional to the inverse of the net heat flux at its exposed surface. True False

F6.1 Piloted ignition occurs when the lower flammable limit is … Read More...
Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage and wings and are located as shown

## Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage and wings and are located as shown

Part A Draw a free-body diagram of the airplane. Draw … Read More...