A small rocket is launched vertically, attaining a maximum speed at burnout of 1.0 102 m/s and thereafter coasting straight up to a maximum altitude of 1528 m. Assuming the rocket accelerated uniformly while the engine was on, how long did it fire?
and how high was it at engine cutoff?

Question

A small rocket is launched vertically, attaining a maximum speed at burnout of 1.0 102 m/s and thereafter coasting straight up to a maximum altitude of 1528 m. Assuming the rocket accelerated uniformly while the engine was on, how long did it fire? 
and how high was it at engine cutoff?

anonymous · Answer

First you'll want to find what altitude the rocket was at engine cutoff. You know that once it starts coasting the only force acting on it will be gravity, so its acceleration will be g. You can find the distance the rocket coasted for from the equation$$v_f^2-v_i^2=2*a*D$$Where the final velocity is 0, the initial velocity is given, and a=-9.8. The rockets altitude is 1528 - D
Then you can find the time the rocket fired from$$D=(v_f-v_i)*t/2$$This time D is your altitude at engine cutoff, the final velocity is given and the initial velocity is 0.