Chapter 1, Problem 6PS

To determine

To find: The coordinates of the point and the equation for the path of the ball.

Answer to Problem 6PS

The equation for the path of the ball is $-3.5y=6x-64$ and $3.5y=6x-8$ .

Explanation of Solution

Given:

The coordinates of the ball are $\left(2.5,2\right)$ and the coordinate for the hole is $\left(9.5,2\right)$ .

Calculation:

Consider the coordinate at which the professional wants the ball is $\left(x,y\right)$ as shown below,

The $x$ coordinate of the point must be at the midpoint of the $x$ coordinate of the ball and the hole that is,

  $\begin{array}{c}x=\frac{2.5+9.5}{2}\\ =6\end{array}$

The $y$ coordinate has the maximum limit of $8\text{ft}$ , thus the $y$ coordinate is equal to $8$ .

The ball first moves from the points $\left(2.5,2\right)$ to coordinates $\left(x,y\right)$ and then the ball moves from the point $\left(x,y\right)$ to $\left(9.5,2\right)$ .

The equation for the line that passes through the two point is,

  $\frac{y-y_2}{x-x_2}=\frac{y_2-y_1}{x_2-x_1}$

Then the equation of the line passing through $\left(2.5,2\right)$ and $\left(x,y\right)$ is,

  $\begin{array}{l}\frac{y-8}{x-6}=\frac{8-2}{6-2.5}\\ 3.5y=6x-8\end{array}$

Then the equation of the line passing through $\left(9.5,2\right)$ and $\left(x,y\right)$ is,

  $\begin{array}{l}\frac{y-8}{x-6}=\frac{8-2}{6-9.5}\\ -3.5y=6x-64\end{array}$

Thus, the equation for the path of the ball is $-3.5y=6x-64$ and $3.5y=6x-8$ .