Question

A pool player located at x wants to shoot the white ball off the top cushion and hit the red ball dead center. he knows from physics that the white ball will come off a cushion at the same angle as it hits a cushion. where on the top cushion should he hit the white​ ball?

Answer 1

We construct two triangles: ABC and CDE, where

A - position of of white ball
B - position on bumper directly above white ball
C - position on bumper where the 2 red arrows meet
D - position on bumper directly above red ball
E - position of red ball

AB = 3 ft
BC = x
CD = 5-x
DE = 1.8 ft

△ABC and △EDC are both right angled (at ∠ABC and ∠EDC respectively)
△ABC and △EDC have congruent angles (∠ACB and ∠ECD)
Therefore, △ABC is similar to △EDC

By similar triangles:
BC/DC = AB/ED
x/(5-x) = 3/1.8
1.8x = 3(5-x)
1.8x = 15 - 3x
4.8x = 15
x = 3.125

So player should hit the white ball 3.125 ft to right of point B.
Point B is 1 ft to right of upper left corner.

Therefore, player should hit white ball 4.125 ft to right of upper left corner.