A body of mass m_{1} moving with an unknowm 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}=0.5m_{1} and v_{3}=0.5v_{1}, the v_{1} is :

 

  • Option 1)

    v_{4}-\frac{v_{2}}{2}

  • Option 2)

    v_{4}-v_{2}

  • Option 3)

    v_{4}-\frac{v_{2}}{4}

  • Option 4)

    v_{4}+v_{2}

Answers (1)

before collision:

after collision:

\left ( P_{initial} \right )_{total}=\left ( P_{final} \right )_{total}

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_{2}=0.5m_{1}  &  v_{3}=0.5 v_{1}

\hat{i}\left ( m_{1}v_{1}+0.5 m_{1}v_{2} \right )=\hat{i}\left ( m_{1}v_{3}+0.5 m_{1}v_{4} \right )

v_{1}+0.5 v_{2}=v_{3}+0.5v_{4}

v_{1}+0.5 v_{2}=0.5v_{1}+0.5v_{4}\;\;\;\;\;\;\;\;\ \left ( v_{3}=0.5 v_{1} \right )

0.5v_{1}+0.5v_{2}=0.5v_{4}

v_{1}+v_{2}=v_{4}

v_{1}=v_{4}-v_{2}


Option 1)

v_{4}-\frac{v_{2}}{2}

Option 2)

v_{4}-v_{2}

Option 3)

v_{4}-\frac{v_{2}}{4}

Option 4)

v_{4}+v_{2}

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