Question

An object is launched from 180 feet above the ground. The function that models the height, in feet, of the object after t seconds is given by
f(t)= -16t^2+96t+180. Which statement is true?

A. The object will obtain a maximum height of 180 feet.

B. The object will obtain a maximum height of 324 feet.

C. The object will obtain a maximum height after 6 seconds.

D. The object will obtain a maximum height after 7.5 seconds.

Answer 1

I believe the answer is D

Answer 2

The maximum height is the greatest height an object can reach before falling. The object will obtain a maximum height of 324 feet.

What is the maximum height of an object?

The maximum height is the greatest height an object can reach before falling.

Given the equation that represents the height of an object as:

f(t)= -16t^2+96t+180

Differentiate

f'(t) = -32t + 95

The time it takes to reach the maximum height is expressed as:

0 = -32t + 96

32t = 96

t = 3secs

Determine the maximum height

f(t)= -16t^2+96t+180

f(3)= -16(3)^2+96(3)+180

f(3) = -144 + 180 + 288

f(3) = 324feet

Hence the object will obtain a maximum height of 324 feet.

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