Fourteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -18ft/s in 5 s. A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a (t) = 60t at which time the fuel is exhausted and it becomes a freely "falling" body. The rocket then "floats" to the ground at that rate.
1. Calculate the position function s and the velocity function v (for all times t). Sketch the graphs of s and v.
2. At what time does the rocket reach its maximum height?