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?

Answer 1

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.