Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 44.1 m/s2 . The acceleration period lasts for time 8.00 s until the fuel is exhausted. After that, the rocket is in free fall.
Part A
Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2

Answer 1

Initial speed:

$$v=at$$

Initial height:

$$h=0.5at^2$$

From the conservation of energy:

$$mgH=mgh+0.5mv^2\to H=gh+0.5v^2$$

$$H=0.5agt^2+0.5(at)^2=0.5at^2(a+g)$$

$$H=0.5(44.1)(8)^2(44.1+9.8)=76100\ m=76.1\ km$$