A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 s. The rocket then "floats" to the ground at that rate. (a) Determine the position functions and the velocity function v (for all times t). if 0 ≤ t≤ 3 v(t) = if 3 <t≤ 21 if 21 < t ≤ 26 if t > 26 if 0 st ≤ 3 if 3 < t≤ 21 s(t) = if 21 < t≤ 26 ift > 26 (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