A rocket with mass .25 kg is launched straight up. Starting from rest at t=0 the

Question

A rocket with mass .25 kg is launched straight up. Starting from rest at t=0 the engine exerts an upward force F=10N until 10 s and then burns out. Upon reaching maximukm height the rocket deploys a parachute and descends vertically to ground. Ignore air trag while rocket is moving up. While rocket falls to ground it reaches a terminal velocity of 4.2m/s
Determine velocity of rocket at t=2 sec
Determine maximum height above ground reached by rocket.
Calculate work done by air drag force during descent to the ground then use this to calculate average force exerted on rocket by air drag

Explanation / Answer

F=10N
so, a= F/m =10/.25 = 40 m/s2
for the first 10s, distance travelled,d1 = .5*(40-9.8)*10^2 = 1510m

final velocity reached after 10s = (40-9.8)*10 = 302 m/s

so, total distance travelled upto the highest point of its flight = 1510 + 302^2/(2*9.8) = 6163.3 m <---max height attained abv ground

velocity at t=2s,  = (40-9.8)*2 = 60.4 m/s  <----answer

work done by air drag force during descent to the ground = - .25*9.8*6163.3 = 15100.1 J

so, average force = 15100.1/(6163.3) = 2.45 N

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