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.

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Solution

Step 1: Given information
Mass, $m_{1} = 100 g m_{2} = 200 g$
Velocity, $v_{1} = 2 m / s v_{2} = 1 m / s v_{3} = 1.67 m / s$
Step 2: Formula used
If no external force is acting on a system, the total momentum of the system remains constant.
The momentum before the collision will be the same as the momentum after the collision.
$m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{3} + m_{2} v_{4}$
Here,
$m_{1}$ and $m_{2}$ are the masses of the objects.
$v_{1}$ and $v_{2}$ are the velocities of the respective objects before the collision.
$v_{3}$ and $v_{4}$ are the velocities after the collision.
Step 3: Calculate the velocity of the second object after the collision
$\Rightarrow (100 g \times 2 m / s) + (200 g \times 1 m / s) = (100 g \times 1.67 m / s) + (200 g \times v_{4}) 400 = 167 + 200 \times v_{4} 200 \times v_{4} = 233 v_{4} = 1.165 m / s$
Hence, the velocity of the second object after the collision is $1.165 m / s$ .

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