A toy rocket, launched from the ground, rises vertically with an acceleration of 32 m/s^2 for 4.1 s until its motor stops. Disregarding any air resistance, what maximum height above the ground will the rocket achieve? The acceleration of gravity is 9.8 m/s^2. Answer in units of k

Answer 1

as usual,

s = 1/2 at^2

Since g is acting downward, the net acceleration is 32-9.8 = 22.2 m/s^2 upward

s = 1/2 * 22.2 * 4.1^2 = 186.6m

Actually, the question is poorly worded, since it implies that the net acceleration is 32 m/s^2, even after including the effects of gravity. Instead, it should have been stated that the rocket motor provided the 32 m/s^2 acceleration, from which gravity's effect must be subtracted.

Answer 2

Vi = a t = 32 * 4.1 = 131 m/s at burn out
h = (1/2)32 (4.1)^2 = 269 meters at burn out
then

v = Vi + a t
at top v = 0
0 = 131 - 9.8 t
t = 13.4 seconds coasting up

h = 269 + 131 (13.4) -4.9 (13.4)^2

Answer 3

I think they mean total acceleration up

Answer 4

As usual, go with Damon. He tends to think things through more carefully.