Chapter 9.6, Problem 5MRPS

Solution

To state: The distance d that an outfielder must throw at G the ball to make an out at home plate if on a baseball field, the pitcher at P is 60.5 feet from home plate at H and 95 feet from an arc where the outfield grass begins. A ball is hit ${25}^{\circ }$ to the right of the pitcher’s mound and travels to the edge of the grass.

  

The resultant answer is $53.06\text{ feet}$ .

Given information:

The pitcher at P is 60.5 feet from home plate at H and 95 feet from an arc where the outfield grass begins. A ball is hit ${25}^{\circ }$ to the right of the pitcher’s mound and travels to the edge of the grass.

Explanation:

The pitcher at P is 60.5 feet from home plate at H and 95 feet from an arc where the outfield grass begins.

Now consider the figure:

  

Use the law of cosines to find the distance d ,

  $\begin{array}{c}{d}^2={\left(60.5\right)}^2+{\left(95\right)}^2-2\left(60.5\right)\left(90\right)\cos 25\\ d^2=12685.25-10890\cos 25\\ d^2\approx 2815.56\\ d\approx 53.06\end{array}$

Therefore, the outfielder must throw at a distance of about 53.06 feet to make an out at home plate.