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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?

Respuesta :

meerkat18
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. 

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