physics
posted by Christina on .
A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 91.9 m/s2 for 1.53 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

First calculate the burnout velocity (Vbo) and altitude (Hbo).
Vbo = a*t = 91.9*1.53 = 140.6 m/s
Hbo = (a/2)t^2 = 107.6 m
The additional distance Hco that the rocket coasts upward can be calculated assuming conservation of energy.
g*Hco = Vbo^2/2
Hco = 1008.6 m
Hmax = Hbo + Hco
Constant rocket mass is being assumed.