Chapter 5, Problem 15QC

To determine

Find the time taken by the ball to reaches the ground.

Answer to Problem 15QC

The time taken by the ball to reaches the ground is $1.768\text{seconds}$ .

Explanation of Solution

Given:

The given model is $h=-16t^2+50$ , where $h$ represents the height of an object after $t$ seconds.

Calculation:

For the ground $h=0$ .

Substitute the value of $h=0$ in the given model.

  $\begin{array}{l}h=-16t^2+50\\ \Rightarrow 0=-16t^2+50\end{array}$

Subtract $50$ from both sides.

  $\begin{array}{l}\Rightarrow 0-50=-16t^2+50-50\\ \Rightarrow -50=-16t^2\end{array}$

Divide both sides by $-16$ .

  $\begin{array}{l}\Rightarrow \frac{-50}{-16}=\frac{-16}{-16}{t}^2\\ \Rightarrow \frac{25}{8}=t^2\\ \Rightarrow \sqrt{\frac{25}{8}}=\sqrt{t^2}\\ \Rightarrow 1.7677=t\\ \Rightarrow t\approx 1.768\text{seconds}\end{array}$

Hence the time taken by the ball to reaches the ground is $1.768\text{seconds}$ .