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  3. Physics
  4. A body of mass m1 moving with an unknown velocity of v1 hati, undergoes a collinear collision with a body of mass m2 moving with a velocity v2 hati . After collision, m1 and m2 move with velocities of v3 hati and v4 hati , respectively. If m2 = 0.5 m1 and v3 = 0.5 v1 , then v1 is :-

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Q. 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 $v_2 \hat{i}$ . After collision, $m_1$ and $m^2$ move with velocities of $v_3 \hat{i}$ and $v_4 \hat{i}$ , respectively.
If $m_2 = 0.5 \; m_1$ and $v_3 = 0.5 v_1$ , then $v_1$ is :-

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Solution:

Applying linear momentum conservation $m_{1}v_{1} \hat{i} + m_{2} v_{2} \hat{i} = m_{1} v_{3 } \hat{i } +m_{2} v_{4} \hat{i} $
$ m_{1}v_{1} + 0.5 m_{1}v_{2} = m_{1}\left(0.5v_{1}\right) + 0.5 m_{1}v_{4} $
$ 0.5 m_{1}v_{1} = 0.5 m_{1} \left(v_{4}-v_{2}\right) $
$ v_{1} =v_{4} -v_{2} $