Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 53.9 m/s^2. The acceleration period lasts for time 5.00 s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height y_max reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s^2. Write your answer numerically in units of meters.

Answer 1

$\large u=0m/s$

Initial acceleration

$\large a_{in}=53.9m/s^2$

$\large t=5.0s$

$\large v=u+at$

$\large v=53.9m/s^2\times 5sec=269.5m/s$ until this velocity it will accelerate

$\large h_{acc}=\frac{1}{2}a_{in}t^2$

$\large h_{acc}=673.75$

Now it will be the motion under gravity

$\large v_f=0$

$\large (269.5)^2=2\times 9.8\times h_{f}$

$\large h_{f}=3705.625m$

$\large y_{max}=H_{total}=h_{acc}+h_f$

$\large y_{max}=673.75m+3705.625$

$\large y_{max}=4379.375m$