A body of mass `m _ 1 ` moving with an unknown velocity of ` v _ 1 hati ` , undergoes a collinear collision with a body of mass ` m _ 2 ` moving with a velocity ` v _ 2 hati `. After collision ` m _ 1 and m _ 2 ` move with velocities of ` v _ 3 hati and v _ 4 hati , ` respectively. If ` m _ 2 = 0.5 m _ 1 and v _ 3 = 0.5 v _ 1` , then ` v _ 1 ` is ` v _ 4 - (v _ 2 ) / (x ) `, where ` x ` is _________.

Explanation

Conserving momentum
` m _ 1 vecv _ 1 + m _ 2 vecv _ 2 = m _ 1 vecv _ 3 + m _2 vecv _ 4 `
` m _ 1 v _ 1 + ( m _ 1 v _ 2 ) /(2) = m _ 1 ( v _ 1 )/(2) + ( m _ 1 ) /(2 ) v _ 4 `
` rArr ( v _ 1 ) /(2) = ( v _ 4 - v _ 2 )/(2 ) rArr v _ 1 = v _ 4 - v _ 2 " " = v _ 4 - 7 ( v _ 2 ) / ( x ) `