Chapter 1.7, Problem 19Q

Solution

To find: the time taken by the ball in the air.

The ball is in the air for 1.7 seconds.

Given:

A student drops a ball from a school roof 45 feet above the ground.

Concept used:

When the object is dropped, its height $h$ (in feet) above the ground after $t$ seconds can be modeled by the function $h=-16t^2+h_0$ , where $h_0$ is the object’s initial height.

Calculation:

Consider the function, $h=-16t^2+h_0$ .

Substitute $0$ for $h$ and 45 for $h_0$ , it follows that

  $\begin{array}{c}0=-16t^2+45\\ 16t^2=45\\ t^2=2.8125\\ t=\pm \text{1}\text{.677}\\ t\approx \pm 1.7\end{array}$

Since time cannot be negative, therefore reject $-\text{1}\text{.7}$ .

Hence the ball is in the air for 1.7 seconds.