A weather rocket is fired vertically upwards. The rocket motor burns for a given time, giving the rocket upward acceleration, a, during that time. Assume that air resistance and g variations with altitude are negligible. Show that the ratio: time to reach greatest height/ time to return to earth from greatest height = (1+(g/a)) Please help with this question.

Question

anonymous · Answer

Take the rocket's initial velocity to be zero. Say the upward acceleration lasts for time T. After T, the altitude is (1/2)aT^2 and the velocity is aT. From this time on, it experiences downward acceleration g. How much additional time does it take to get from time T until the altitude is zero again?