A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds isa(t) =54t, at which time the fuel is exhausted and it becomes a freely "falling" body.Thirteenseconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to13

ft/s in 5 s. The rocket then "floats" to the ground at that rate.

(a) At what time does the rocket reach its maximum height?

(b)What is that height? (Round your answer to the nearest integer.)

(c) At what time does the rocket land? (Round your answer to one decimal place.)