Assignment:
A model rocket is fired vertically upward from rest. It's acceleration for the first three seconds is a(t)=60t at which time the fuel is exhausted and it becomes a free falling body. After 17 seconds, the rocket's parachute opens and the velocity slows linearly to -18 ft/sec in 5 seconds. The rocket then floats to the ground at that rate.
a) Find the position function s and the velocity function v for all times t. Sketch the graphs of s and v.
b) At what time does the rocket reach its maximum height?
c) At what time does the rocket hit the ground?
Recall that acceleration due to gravity is -32ft/sec^2.
Provide complete and step by step solution for the question and show calculations and use formulas.