A model rocket is fired vertically upward from rest. Itsacceleration for the first three seconds is a(t)=96t, at which timethe fuel is exhausted and it becomes a freely \"falling\" body. 1919seconds later, the rocket's parachute opens, and the (downward)velocity slows linearly to −16 ft/s in 5 s. The rocket then\"floats\" to the ground at that rate.
(a) Determine the position function s and the velocity functionv(for all times t).
| v(t)= | |   | if 0≤t≤3 | |    | if 3 | |    | if 22 | |   | if t>27 |
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| s(t)= | |    | if 0≤t≤3 | |   | if 3 | |    | if 22 | |    | if t>27 |
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(b) At what time does the rocket reach its maximum height?(Round your answer to two decimal places.)
What is that height? (Round your answer to the nearestinteger.)
(c) At what time does the rocket land? (Round your answer to onedecimal place.)
