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 -18 ft/s in 5 s. The rocket then "floats" to the ground at that rate.
(b) At what time does the rocket reach its maximum height? (Give your answer correct to one decimal place.)
What is that height? (Give your answer correct to the nearest whole number.)
(c) At what time does the rocket land? (Give your answer correct to one decimal place.)