Consider the collision depicted in figure to be between two billiard balls are equal masses `m_(1)=m_(2)` . The first ball is called the cue while the second ball is called the target . The billiard player wants to 'sink ' the target ball in a corner pocket , which is at angle `theta_(2) = 37^(@)` .Assume that the collision is elastic and that friction and rotational motion are not important . Obtain `theta_(1)` .

Explanation

From the law of conservation of momentum ,
`m_(1)vec(v_(li)) =m_(2)vec(v_(2i))=m_(1)vec(v_(1f) )+m_(2)vec(v_(2))f`
but `m_(1)=m_(2) and vec(v_(2i)) =0 `
`:. v_(li)^(2) =(vec(v_1f)+vec(v_(2f))).(vec(v_(1f))+vec(v_(2f)))`
` :. v_(li)^(2) =v_(1f)^(2)+v_(2f)^(2) +2vec(v_(1f)).vec(v_(2f))`
` :. v_(li)^(2) = v_(1f)^(2) +2v_(1f)v_(2f)cos (theta+37^(@))....(1)`.