Question

A diver dives into a swimming pool from the diving board. His height in feet is given by y(t) = −16t2 + 32t + 20, where t is the time in seconds. The horizontal distance in feet of the diver from the diving board is given by x(t) = 2t. What horizontal distance will the diver travel before he hits the water?

a. 5.0 ft
b. 2.5 ft
c. 2.41 ft
d. 0.5 ft

Answer 1

The horizontal distance when the diver travel before he hits the water is: a. 5.0 ft.

The vertical height equation

y(t)=-16t²+32t+20

when t=0; y(0)=16·0²+32·0+20

First step is to calculate t when y(t)=0

0=-16t²+32t+20

-16t²+32t=-20

t²-2t=5/4

Second step

t²-2t+(-2/2)²=5/4+(-2/2)²

t²-2t+1=5/4+5/4

(t-1)²=9/4

(t-1)²=(3/2)²

t-1=3/2

t=5/2

Third step is to find the  horizontal distance

When t=5/2

x(t)=2t

x(5/2)=2×(5/2)

x(5/2)=5ft

Inconclusion the horizontal distance when the diver travel before he hits the water is: a. 5.0 ft

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