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.

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Solution

Step 1: Given
$m_{1} = 100 g = 0.1 kg, m_{2} = 200 g = 0.2 kg$ , $u_{1} = 2 {ms}^{- 1}, u_{2} = 1 {ms}^{- 1}, v_{1} = 1.67 {ms}^{- 1}, v_{2} =$ ?
Step 2: The velocity of the second object
According to the law of conservation of momentum.
Total momenta = Total momenta
before collision after collision
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
or $0.1 \times 2 + 0.2 \times 1 = 0.1 \times 1.67 + 0.2 v_{2}$
or
$0.4 = 0.167 + 0.2 v_{2}$
or
$v_{2} = \frac{0.4 - 0.167}{0.2}$
$= 1.165 {ms}^{- 1}$

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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.

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