Question

A billiards-ball is at point A on a billiards-table whose dimensions are given in fig. At what angle should the ball be struck so that it should rebound from two cushions and go into pocket B? Assume that in striking the cushion, the ball’s direction of motion changes according to the law of reflection of light from a mirror, i.e., the angle of reflection equals the angle of incidence.

• A. $\frac{a - 2c}{b}$
• B. $\frac{2a - c}{b}$
• C. $\frac{2a - c}{2b}$
• D. $\frac{a}{b} - \frac{a}{2c}$

Answer 1

Answer: (C)

$\frac{2a - c}{2b}$

Answer 2

Let us resolve the velocity v imparted to the ball into component parallel with the sides of the table and consider the path of a ball as shown, for example, in the diagram (fig.).

We obtain two equations, evident from the diagram :

$\frac{2a - c}{t}$ = v cos a, $\frac{2b}{t}$ = v sin a,

From these equations we get :

cot a = $\frac{2a - c}{2b}$,

i.e., we find angle a, at which the ball must be struck. The value for the velocity v which is imparted to the ball plays no part at all.