Question

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 1

The ball will take approximately 2.165 seconds.

Explanation:

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

`-16\cdot t^(2)+75 = 0` (1)

`16\cdot t^(2) = 75`

`t = \sqrt{(75)/(16) }`

`t \approx 2.165\,s`

The ball will take approximately 2.165 seconds.