Chapter 13.7, Problem 28PSD

To determine

To find: The point on the y axis that should be aimed.

Answer to Problem 28PSD

The point that should be aimed is $\left(0,\frac{35}{11}\right)$ .s

Explanation of Solution

Given:

The green ball is at $\left(3,1\right)$ and the grey billiard ball is at $\left(8,9\right)$ .

Calculation:

Consider the point that is should be aimed is $\left(0,y\right)$ ,

Then,

  $\begin{array}{l}\tan a=\frac{\left(y-1\right)}{3}\\ \tan b=\frac{\left(9-y\right)}{8}\end{array}$

Then, by the law of reflection.

  $\begin{array}{l}\frac{\left(y-1\right)}{3}=\frac{\left(9-y\right)}{8}\\ 8y-8=127+3y\\ y=\frac{35}{11}\end{array}$

Thus, the point that should be aimed is $\left(0,\frac{35}{11}\right)$ .