A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t at which time the fuel is exhausted and it becomes a freely "falling" body. 19 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -16 ft/s in 5 s. The rocket then "floats" to the ground at that rate. At what time does the rocket reach its maximum height? And what is that height?

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t at which time the fuel is exhausted and it becomes a freely "falling" body. 19 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -16 ft/s in 5 s. The rocket then "floats" to the ground at that rate. At what time does the rocket reach its maximum height? And what is that height?