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 18 m/s2. After 26 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 20 km above the ground.

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

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

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

Explanation / Answer

Part A)

Find the height traveled during the thrust

Apply d = vot + .5at2

d = 0 + .5(18)(26)2

d = 6084 m

Now we need the velocity at that point

vf = vo + at

vf = 0 + (18)(26)

vf = 468 m/s

Now find how much higher it goes from there

vf2 = vo2 + 2ad

0 = 4682 + 2(-9.8)(d)

d = 11175 m

Total height = 11175 + 6084 = 17259 m (17.2 km)

Part B)

Time to go the additional height

vf = vo + at

0 = 468 + (-9.8)(t)

t = 47.76 s

Time to fall all the way down

d = vot + .5at2

17259 = 0 + (.5)(9.8)(t2)

t = 59.3 sec

Total time = 59.3 + 47.76 + 26 = 133.1 sec (2 mins and 13 sec)

Part C)

vf = vo + at

vf = 0 + (9.8)(59.3)

vf = 581.6 m/s (Your answer key may want this as a negative since its downward)

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