A ball is dropped from a 75 foot tall tower, and the height of the ball (in feet) can be represented by the equation h = —16t^2 + 75 where t is time (in seconds). Determine the amount of time it will take for the ball to hit the ground. Round your answer to the nearest hundredth of second. (Show Work)

Answer:

The ball will take approximately 2.165 seconds.

Step-by-step explanation:

The height of the ball is represented by the function [tex]h(t) = -16\cdot t^{2}+75[/tex], the time taken by the ball to hit the ground is a value of [tex]t[/tex] such that [tex]h(t) = 0[/tex], we proceed to solve the following equation for [tex]t[/tex]:

[tex]-16\cdot t^{2}+75 = 0[/tex] (1)

[tex]16\cdot t^{2} = 75[/tex]

[tex]t = \sqrt{\frac{75}{16} }[/tex]

[tex]t \approx 2.165\,s[/tex]

The ball will take approximately 2.165 seconds.

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