Chapter 13.4, Problem 30PPS

To determine

To Prove: The horizontal distance the ball travels in the air will be the same for $\theta =45°+A$ as for $\theta =45°-A$ .

Explanation of Solution

Given:

On average, a place kick travels about 15 yards farther than a punt, assuming the kicker is at least 13 years old.

Calculation:

Consider the equation for the distance that the soccer ball goes in the air if it is not blocked is,

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

Then,

  $d=\frac{v^2\sin 2\theta }{g}$

Substitute the values in the above equation as,

  $\begin{array}{c}d=\frac{{\left(95\right)}^2\sin 2\left(45°+A\right)}{32.2}\\ =280.28\sin \left(90°+2A\right)\\ =-280.28\cos 2A\end{array}$ ……………………………… (1)

Consider the equation for is $\theta =45°-A$ ,

  $\begin{array}{c}d=\frac{{\left(95\right)}^2\sin 2\left(45°-A\right)}{32.2}\\ =280.28\sin \left(90°-2A\right)\\ =280.28\cos 2A\end{array}$

From the above equation and from equation (1) it is proved that the distance covered by the ball for $\theta =45°+A$ and $\theta =45°-A$ are in the second direction.