A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 92.9 m/s2 for 1.85 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?
thrust stage
v = a t = 92.9*1.85 = 172 m/s
h = (1/2) a t^2 = (1/2)(92.9)(1.85)^2 = 159 m
coast stage
0 = 172 - 9.81 t
t = 17.5 seconds to stop
h = 159 + 172 t -(1/2)9.81*t^2
h = 159 + 172(17.5) - 4.9(17.5^2)
= 1670 m approximately