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

Answer:

The ball will take approximately 2.165 seconds.

Step-by-step 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)

$16\cdot t^{2} = 75$

$t = \sqrt{\frac{75}{16} }$

$t \approx 2.165\,s$

The ball will take approximately 2.165 seconds.