A rocket, initially at rest on the ground, accelerates straight upward from rest

Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 29.4m/s2 . The acceleration period lasts for time 9.00s until the fuel is exhausted. After that, the rocket is in free fall.

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.

Note: There are two parts to the question: one where the rocket has fuel, and two, the continued motion after the fuel is exhausted.

Explanation / Answer

acceleration 29.4m/s2 lasts for 9 seconds

so velocity at end of 9 sec=V1=u+at=29.4*9=264.6m/s

distance travelled in 9 sec=0.5*a*t^2=0.5*29.4*81=1190.7m

At max height V=0

so 0=264.6-9.8t

so t=27 sec

distance travelled in next 27 sec=264.6*27-0.5*9.8*27^2=3572.1m

so max height=1190.7+3572.1=4762.8m

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