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 16 m/s2. After 21 s, the engine shuts off and the rocket continues rising (in free fall) 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 12 km above the ground. What is the highest point your rocket reaches? Did you reach your height goal? Yes No Determine the time the rocket is in the air. Find the speed of the rocket just before it hits the ground.

Explanation / Answer

distance covered in 21 sec = ut+ 0.5a t^2
= 0+0.5*16*21^2 = 3528 m
velocity at 21 sec,v = u+at = 0 + 21 * 16 = 336 m/s
distance covered in free fall

now a=-g=-10 and v=0
v2 = u2 -2as
0=336^2-2*10*s
s=5644.8 m
Total height reached = 5644.8+3528 = 9127.8 m = 9.1278 km Ans (a)
No the height goal is not reached

time to reach highest point in freefall,t1=> v=u + at1 => 0 = 336-10t1 => t1 = 33.6 s

time to reach ground in free fall,t2 using s = ut + 0.5 at2 where s=- 9127.8 m and u = 0

-9127.8=0.5(-10)t22 => t2=42.73 s

total time rocket in air,t=21+t1+t2 = 97.33 s Ans(b)

velocity at bottom, v=u+at2 => v= 0 -(10)42.73 => v=427.3 m/s Ans(c)

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