Robert has just bought a new model rocket, and is trying to measure its flight c

Question

Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 13.2 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range-finder to meaure that the height of the rocket when the engine cuts off is 12.4 m. He also measures the rocket's peak height, which is 16.9 m. If the rocket has a mass of 0.763 kg, how much work is done by the drag force on the rocket during its ascent?

Explanation / Answer

There are 3 different stages. There's lift-off, engine cutoff and peak height. Lets call these points 1, 2 and 3 respectively.

Use work energy between engine cut off and peak height first to determine kinetic energy at peak height.

KE2 + mgy2 = KE3 + mgy3

But KE3 = 0 since at peak height speed is zero.
Ke2 = mg(y3-y2)

Now that we have kinetic energy at point two, use the work energy theorem:

Ke1 + mgy1 + Wrocket + Wwind = KE2 + mgy2

KE1 = 0 since it begins at rest:
Wrocket + Wwind = KE2 + mg(y2-y1)

Wind work is negative, since F*D is negative. (The force acting on the object is opposite of direction of travel.)
Wr -Ww = KE2 + mg(y2-y1)

Solve for work due to wind:
force x distance = work done by rocket engine
PE gain = mgh

work done by rocket engine - PEgain = work done by drag forces

(13.2 x12.4 - 0.763 (9.8)16.9 = work done by drag forces

work done by drag forces =37.31194 J

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