A and B are two identical balls. A moving with a speed of `6m//s`, along the positive X-axis, undergoes a collision with B initially at rest. After collision, each ball moves along directions making angles of `+-30^(@)` with the X-axis. What are the speeds of A and B after the collision ? I s this collision perfectly eleastic ?

Explanation

Here, `u=6ms^(-1), theta =30^(@), phi=30^(@), upsilon_(1)=? upsilon_(2)=?`
Using the law of conservation of linear momentum along X-axis
`u=upsilon_(1)cos theta +upsilon_(2)cosphi`
`6=upsilon_(1)cos 30^(@)+upsilon_(2)cos 30^(@)=(upsilon_(1)+upsilon_(2))(sqrt(3))/(2)` ...(i)
Using the law of conservation of linear momentum along Y-axis
`0=upsilon_(1)sintheta-upsilon_(2)sinphi=upsilon_(1)sin 30^(@)-upsilon_(2)sin 30^(@)=(upsilon_(1)-upsilon_(2))/(2):. upsilon_(1)=upsilon_(2)`
From (i), `upsilon_(1)+upsilon_(2)=(12)/(sqrt(3)), 2upsilon_(1)=(12)/(sqrt(3)), upsilon_(1)=(6)/(sqrt(3))xx(sqrt(3))/(sqrt(3))=2sqrt(3)ms^(-1)`
Hence `upsilon_(1)=upsilon_(2)=2sqrt(3)ms^(-1)`
As `theta+phi!=90^(@):.` The collision is NOT perfectly elastic.