A kid has a 3.5 kg toy rocket that gets ignited and shoots straight up to a heig

Question

A kid has a 3.5 kg toy rocket that gets ignited and shoots straight up to a height of 50 m. As it is falling back down, when it gets to a speed of 12 m/s, a small parachute abruptly and automatically pops out, and the rocket now falls all the way to the ground with a terminal velocity of 12 m/s. On the way up, air resistance and friction are negligible, but obviously not once the parachute deploys. Several questions refer to the following graphs. Which graph best shows the potential energy as a function of height, starting at the top of the trajectory? Which graph best shows the kinetic energy as a function of height, starting at the top of the trajectory? Which graph best shows the total mechanical energy as a function of height, starting at the top of the trajectory? Which graph best shows the total mechanical energy as a function of height, starting at the bottom of the trajectory and ending at the top? While the rocket is rising, (A) the momentum of the escaping gases exceeds the momentum of the rocket (B) the momentum of the escaping gases is less than the momentum of the rocket (C) the momentum of the escaping gases equals the momentum of the rocket.

Explanation / Answer

1) the potential energy is a function of height h

P.E = mgh, there fore P.E proportional to h so it is a linear decrease

2) when object comes down the kinetic energy increases but after the parachute is open then no increase in velocity so the kinetic energy is constant

3) the mechanical enrgy is constant as long as no air resistance is present but when air resistance is considered the potential enrgy decreases and kinetic energy remains constant so mechanical energy also decreases

4) when the object moves up there was no air resistance so the total mechanical energy is constant

5) the rate momentum of both is same , this is because from Newton's third law the exerted on each other is same

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