A body of mass `m_(1)` moving with an unknown velocity of `v_(1)hat i`, 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)=0.5v_(1)`, then `v_(1)` is :

Options

A. `v_4 - (v_2)/2`
B. `v_4 - v_2`
C. `v_4 - (v_2)/(4)`
D. `v_4+ v_2`

Answer

B

Explanation

Conserving momentum
`m_1vecv_1 + m_2vecv_2 = m_1vecv_3 + m_2vecv_4 , m_1v_1 + (m_1v_2)/(2) = m_1 (v_1)/2 + (m_1)/2 v_4 implies (v_1)/2 = (v_4 - v_2)/(2) implies v_1 = v_4 - v_2`.