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.

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Solution

Mass of one of the objects, m₁ = 100 g = 0.1 kg
Mass of the other object, m₂ = 200 g = 0.2 kg
Velocity of m₁ before collision, $v_{1} = 2 m s^{- 1}$
Velocity of m₂ before collision, $v_{1} = 1 m s^{- 1}$
Velocity of m₁after collision, $v_{3} = 1.67 m s^{- 1}$
Velocity of m₂after collision = $v_{4}$
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
$∴ m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{3} + m_{2} v_{4}$
$0.1 (2) + 0.2 (1) = 0.1 (1.67) + 0.2 (v_{4})$
$0.4 = 0.167 + 0.2 v_{4}$
$v_{4} = 1.165 m s^{- 1}$
Hence, the velocity of the second object becomes 1.165 m/s after the collision.

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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.

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