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Question

A model rocket is launched with an initial velocity of 128 ft/s from a height of 85 ft. The height of the rocket, in feet, t seconds after it has been launched is given by the function s(t)=−16t2+128t+85 . Determine the time which the rocket reaches its maximum height and find the maximum height.

Answer 1

To find the time the rocket reaches its maximum height, we evaluate

 

t = -b / 2a

 

where:

a = -16

b = 128

c = 85

 

t = -128 / (2 * -16)

t = -128 / -32

t = 4

 

The rocket reaches its maximum height at 4 seconds.

 

To find the maximum height, evaluate     s(4).