Question 4
Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of $2 m s^{- 1} a n d 1 m s^{- 1},$ respectively. They collide and after the collision, the first object moves at a velocity of $1.67 m s^{- 1}$ . Determine the velocity of the second object.

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Solution

Mass of one of the objects, $m_{1} = 100$ g = 0.1 kg
Mass of the other object, $m_{2} = 200$ g = 0.2 kg
Velocity of $m_{1}$ before collision, $v_{1} = 2 m s^{- 1}$
Velocity of $m_{2}$ before collision, $v_{2} = 1 m s^{- 1}$
Velocity of $m_{1}$ after collision, $v_{3}$ = $1.67 m s^{- 1}$
Velocity of $m_{2}$ after collision $= v_{4}$
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
Therefore, $m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{3} + m_{2} v_{4}$
$2 (0.1) + 1 (0.2) = 1.67 (0.1) + v_{4} (0.2)$
$0.4 = 0.167 + 0.2 v_{4}$
$v_{4}$ = 1.165 $m s^{- 1}$
Hence, the velocity of the second object becomes 1.165 $m s^{- 1}$ after the collision.

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Question 4 Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 ms−1 and 1 ms−1, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 ms−1. Determine the velocity of the second object.