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A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 84t, at which time the fuel is exhausted and it becomes a freely "falling" body. 17 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -6 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 if 3 < t < 20 if 20 < t < 25 if t > 25 v(t) = s(t) = if 0 ≤ t ≤ 3 if 3 < t < 20 if 20 < t < 25 if t > 25
(b) At what time does the rocket reach its maximum height? (Round your answer to two decimal places.) 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.) Question Help: Message instructor Submit Question