Chapter 15, Problem 50CR

a.

To determine

To find: the point where the ball must be striking the barrier at $y=20$ .

Answer to Problem 50CR

  $\left(6,20\right)$ .

Explanation of Solution

Given:

On a miniature golf course, the hole is at $\left(2,18\right)$ and the ball is at $\left(12,2\right)$

as shown below:

  

Calculation:

According to the question,

Reflect H cross $y=13\text{ to }\left(2,8\right)$ . Then reflect $\left(2,8\right)$

Across $y=20\text{ to }\left(2,32\right)$ . Taking the points $\left(12,2\right),\left(x,20\right),\left(2,32\right)$

:

Now,

  $\begin{array}{l}\frac{32-2}{2-12}=\frac{20-2}{x-12}\\ \Rightarrow \frac{30}{-10}=\frac{18}{x-12}\\ \Rightarrow -3=\frac{18}{x-12}\\ \Rightarrow x-12=-6\\ \therefore x=6\end{array}$

Thus, the point where the ball must be striking the barrier at $y=20$ is $\left(6,20\right)$ .

b.

To determine

To check: whether that to go directly to the barrier $y=20$ and then directly to hole.

Answer to Problem 50CR

No.

Explanation of Solution

Given:

On a miniature golf course, the hole is at $\left(2,18\right)$ and the ball is at $\left(12,2\right)$

as shown below:

  

Calculation:

No, by reflecting $\left(2,18\right)$ across $y=20$ to $\left(2,32\right)$ , it is seen that sch a lot would have to strike $y=20$ to $\left(3,20\right)$ .

But this lot is impossible, since it strikes the barrier $x=7$ to $\left(7,12\right)$ and be deflected.