A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 39.2 m/s^2. The acceleration period lasts for time 9.00 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 \rm{m/s^2} .

Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 39.2 m/s^2. The acceleration period lasts for time 9.00 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 \rm{m/s^2} .