A ball moving with a velocity of `12ms^(-1)` collides with another identical stationary ball . After the collision they move as shown in figure . Find the speed of the balls after the collision . Also , decide whether the condition is elastic or not .

Explanation

Suppose the mass of each ball be m . According to the law of conservation of momentum by taking X - components ,
`mv_(1) =mv_(1) cos 30^(@) +mv_(2)cos 30^(@)`
` :. v_(1) = (sqrt(3))/2 v_(1)+(sqrt(3))/2 v_(2)" "....(1)`
Taking Y - components
` p = mv_(1) sin 30^(@) - mv_(2) sin 30^(@)`
` 0 = (v_(1))/2 - (v_(2))/2 `
` :. 0 = v_(1)-v_(2)`
` :. ` From equation (1) ,
The velocity before collision `v_(1) =12 m//s and v_(2) = 0 `
` :. ` The kinetic energy of system before collision
`K_(1)=1/2 mv_(1)^(2) +1/2 mv_(2)^(2)`
`K_(1) =1/2 xxmxx (12)^(2)`
` K_(1) =72 m J " "....(1)`
Velocity after collision `v_(1) =4sqrt(3) m//s and v_(2) = 4sqrt(3) m//s `
` :. ` The kinetic after of system after collision .
`K_(2) =1/2 m xx 48 +1/2 m xx 48`
` :. K_(2) =1/2 m xx 48 +1/2 m xx48`
` :. K_(2) = 24 m + 24 m `
` :. K_(2) = 48 m J " ".....(2)`
` :. ` From equation (1) and (2) ,
`K_(2) gt K_(2)` so the kinetic energy is not conserved , the collision is not elastic .