Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m s^{−1} and 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.

#### 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

Velocity of *m*_{2} before collision, v_{2} = 1 m/s

Velocity of *m*_{1 }after collision, v_{3} = 1.67 m/s

Velocity of *m*_{2 }after 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 + 0.2v_{4}

∴ v_{4} = 1.165 m/s

Hence, the velocity of the second object becomes 1.165 m/s after the collision.