A ball moving at `9m *s^(-1)`, collides with an identical ball at rest. After collision, both the balls scatter at `30^@` with the initial direction of motion. Find the velocity of each ball after collision. Does the kinetic energy remain conserved in such a collision ?

Explanation

Let mass of each ball = m. Velocities of the two balls before collision `u_1=9 m*s^(-1) and u_2=0` [Fig.150].
Let their velocities after collision be `v_1 and v_2` respectively.

From the law of conservation of the xand y components of momentum ,
`9m +0 =mv_1 cos 30^@+vm_2 cos 30^@`.......(1)
`and 0= mv_1 sin 30^@ -mv_2 sin 30^@` .......(2)
From (1),
`v_1+v_2=(18)/sqrt(3)`.......(3)
and from (2) ,
`v_1+v_2=0` ......(4)
`therefore` Solving (3) and (4) ,
`v_1=v_2=3sqrt(3) m*s^(-1)`
Initial kinetic energy `=1/2 mu_1^2+1/2 mu_2^2=1/2m(9^2+0) =(81)/(2) m`
Final kinetic energy `=1/2 mv_1^2+1/2 mv_2^2=1/2m(27+27)=27m`
Hence, kinetic energy does not remain conserved in this case.