Particle `1` experiences a perfectly elastic collision with a stationary particle `2`. Determine their mass ratio , if the particles fly symmetrically relative to the initial motion direction particle `1` with angle of divergence `theta = 60^(@)`.

Explanation

By the momentum conservation :
`x-ax is : m_(1) u = m_(1) v_(1) cos 30^(@) + m_(2) v_(2) cos 30^(@)` (i)
`y - ax is : 0 = m_(1) v_(1) sin 30^(@) - m_(2) v_(2) sin 30^(@)` (ii)
`rArr m_(1) v_(1) = m_(2) v_(2)` in (i)
`m_(1) u = m_(1) u = m_(1) v_(1) cos 30^(@) + m_(1) v_(1) cos 30^(@)`
`= 2 m_(1) v_(1) cos 30^(@) = sqrt(3) m_(1) v_(1)`
`v_(1) = (mu)/(sqrt(3))`
`v_(2) = (m_(1))/(m_(2)) v_(1) = ((m_(1))/(m_(2))) (u)/(sqrt(3))`
Since the collision is elastic , `K_(i) = K_(f)`
`(1)/(2) m_(1) u^(2) = (1)/(2) m_(1) v_(1)^(2) + (1)/(2) m_(2) v_(2)^(2)`
`m_(1) u^(2) = m_(1) ((u)/(sqrt(3)))^(2) + m_(2) xx ((m_(1))/(m_(2)))^(2) ((u)/(sqrt(3)))^(2)`