April shoots an arrow upward into the air at a speed of 32 feet per second from a platform that is 32 feet high. The height of the arrow is given by the function h(t) = -16t2 + 32t + 32, where t is the time is seconds. What is the maximum height of the arrow?

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
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Chapter9: Quadratic Equations And Functions
Section9.6: Graph Quadratic Functions Using Properties
Problem 9.104TI: A path of a toy rocket thrown upward from the ground at a rate of 208 ft/sec is modeled by the...
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April shoots an arrow upward into the air at a speed of 32 feet per second from a platform that is 32 feet high. The height of the arrow is given by the function h(t) = -16t2 + 32t + 32, where t is the time is seconds. What is the maximum height of the arrow?

Expert Solution
Step 1

Given that , April shoots an arrow upward into the air at a speed of 32 feet per second and height of the platform is 32 feet . 

The height of arrow, ht=-16t2+32t+32 where t is time in seconds.

Velocity can be found by differentiating the height. 

Vt=h't       =-16×2t+321+0       =-32t+32

At maximum height the velocity will be zero. So the velocity at maximum height can be given as 

Vt=-32t+32     0=-32t+32  32t=32      t=1 

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