# Position functions

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.

https://brainmass.com/math/calculus-and-analysis/working-position-functions-acceleration-velocity-2285

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Let's clarify the relationship between the height s(t), the velocity ...

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This shows how to find position function and maximum height of a rocket.

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