Chapter 8.5, Problem 35E

To determine

To find: the distance travelled by the ball.

Answer to Problem 35E

239.4 feet

Explanation of Solution

Given information:

The formula for distance travelled by the ball is shown below.

  $d=\frac{2v_o^2}{g}\sin \theta \cos \theta$

Here $v_o$ is initial velocity, $g$ is acceleration due to gravity, and $\theta$ is angle measure of initial path of ball with the ground.

  $\begin{array}{c}\theta =65°\\ v_o=100\text{ ft/s}\\ g=32{\text{ ft/s}}^2\end{array}$

Calculation:

Substitute the values in the distance formula and evaluate $d$ as shown below.

  $\begin{array}{c}d=\frac{2v_o^2}{g}\sin \theta \cos \theta \\ =\frac{2{\left(100\text{ ft/s}\right)}^2}{32{\text{ ft/s}}^2}\sin 65°\cos 65°\\ =\frac{{\left(100\text{ ft/s}\right)}^2}{32{\text{ ft/s}}^2}\left(2\sin 65°\cos 65°\right)\\ =\left(312.5\right)\left(\sin 130°\right)\left[\text{Using double angle identity for sine}\right]\\ =239.4\text{ ft}\end{array}$

Thus the distance travelled is 239.4 feet.