physics
posted by Anonymous .
A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 49.0 . The acceleration period lasts for time 6.00 until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 .

find the velocity at 6.0 sec
vf=a t
and the height at six seconds:
h=1/2 a t^2, that height becomes the initial height for the gliding phase
the velocity at the top is zero.
vf=0=vigt solve for t, where vi is the velociyt at 6.0 sec
so time of flight is 6+t
max height=higluiding+vi*(t)1/2 g t^2 where t was found above, and vi is the final velocity at t=6 of the propulsion stage