A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a ( t ) = 54 t , at which time the fuel is exhausted and it becomes a freely "falling" body. 13 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to − 13 ft/s in 5 s . The rocket then "floats" to the ground at that rate.
(a) Determine the position function s and the velocity function v (for all times t).
v(t) =
| if 0 ≤ t ≤ 3
| if 3 < t ≤ 16
| if 16 < t ≤ 21
| if t > 21
s(t) =
| if 0 ≤ t ≤ 3
| if 3 < t ≤ 16
| if 16 < t ≤ 21
| if t > 21
(b) At what time does the rocket reach its maximum height?
s
What is that height? (Round your answer to the nearest integer.)
ft
(c) At what time does the rocket land? (Round your answer to one decimal place.)
s