You have designed a rocket to be used to sample the local atmosphere for polluti

Question

You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 20 m/s2. After 25 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect any effects due to air resistance.) The rocket eventually stops rising and then falls back to the ground. You want to get a sample of air that is 21 km above the ground.

(a) What is the highest point your rocket reaches? (in km)

Did you reach your height goal? If not, what would you change so that the rocket reaches 20 km?

(b) Determine the total time the rocket is in the air. (in s)

(c) Find the speed of the rocket just before it hits the ground. (in m/s)

Explanation / Answer

Initial velocity u = 0 time t= 25 s accletation a = 20 m / s^ 2 speed of the rocket after 25 s is v = u + at = 500 m / s height reached in 25 s is S = ut + ( 1/ 2) at^ 2 = 0 + 6250 m= 6250 m After 25 s : ------------ Initial speed U = v = 500 m / s final speed ( speed at maximum height ) V = 0 accleration a ' = -g =-9.8 m / s^ 2 time taken to reach maximum height t ' = (V-U) / a ' = 51.02 s height reached after 25 s is S ' = U^ 2/ 2g = 12755.1 m (a). Maximum height reached by rocket from ground H = S + S' H = 19005.1 m = 19.0051 km (b). time taken the rocket to reach the ground from maximum height t " = sqrt [ 2H / g] = 62.27 s So, required time T = t+ t ' + t " = 138.29 s (c).the speed of the rocket just before it hits the ground is = sqrt [ 2gH ] = 610.32 m / s

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