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. Fourteen seconds later, the rocket’s parachute opens, and the (downward) velocity slows linearly to – 18ft/s in 5 s. The rocket then “floats” to the ground at that rate.
(a) Determine the position function and the velocity function v (for all times).
Sketch the graphs of and v.
(b) At what time does the rocket reach its maximum height, and what is that height?
(c) At what time does the rocket land?