Chapter 7.3, Problem 32PPS

To determine

To find: the total distance travelled by the ball.

Answer to Problem 32PPS

  $61.4$ .

Explanation of Solution

Given:

A ball is hitting from the time booker on the table and came it to rest at the end of the table.

When the ball is deflected off a smooth surface, the angle formed by the path is concurrent.

  

Calculation:

From the given figure,

  $\begin{array}{l}\angle D=\angle E\{\text{given}}\\ \angle ABD=\angle CBE\{\text{given}}\\ \therefore \Delta ABD\sim \Delta CBE\{\text{by AA-similarity}}\end{array}$ .

Therefore, the corresponding parts of similar triangle is proportion.

  $\begin{array}{l}\frac{AB}{BC}=\frac{AD}{CE}\\ \Rightarrow \frac{34}{BC}=\frac{21.75}{17.5}\{\text{substitutes these value}}\\ \Rightarrow BC=\frac{17.5\times 34}{21.75}\{\text{simplify} }\\ \Rightarrow BC=27.4\end{array}$

Thus, the total distance, $AB+BC=34+27.4=61.4$

Hence, the total distance travelled by the ball is $61.4$ .