Question

a rocket accelerates vertically upward from rest with acceleration a. after 4.0 s, a small object falls from the rocket. the object strikes the ground 6.0 s later. determine the acceleration of the rocket in terms of g.

Answer 1

(9/4)g

Step-by-step explanation:

The distance the rocket travels is given by:

D = v*t + 1/2*a*t^2. Where v is the initial velocity, t is time, and a is the acceleration. We don;t have the distance nor the acceleration, so the best we can do is rearrange for distance, D, since we we will be able to calculate that with information about the falling rocket.

D =(1/2)a(4)^2

D = 8a

If we find D, we can calculate a, the acceleration of the rocket.

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We are told the rocket takes 8 seconds to fall from height D, The relationship between distance and time with a falling object with force g (earth;s gravity) is:

D = v*t + 1/2*a*t^2

The initial velocity is 0 (rocket turns), the force is g, gravity, and time is 6 seconds, We can set that to the distance calculated in the first step: 8a

8a = 0*t + 1/2*g*(6)^2

8a = 1/2*g*36

a = (36/16)g

a = (9/4)g

The rocket's acceleration was (9/4)g