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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)

best_answer

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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