A ball is moving with a speed of 5 m/s and collides with another ball moving with a speed of 1 m/s in the opposite direction. What will be the speed of the second ball if after the collision the first ball comes to rest and the coefficient of restitution is \( {1\over 3}\)?

CONCEPT:

• Collision: An event in which two or more bodies exert forces on each other for a very short time is called a collision.
  • It results in the exchange or transformation of energy.
• Coefficient of restitution: It is the ratio of the final relative velocity between two objects after they collide to the initial relative velocity between two objects before they collide.

Newton's law of restitution: Mathematically, it says

​v2 − v1= − e (u2 − u1)

where u1 is the initial velocity of the first ball, u2 is the initial velocity of the second ball, v1 is the final velocity of the first ball, v2 is the final velocity of the second ball, and e is the coefficient of restitution.

The coefficient of restitution always satisfies 0 ≤ e ≤ 1. 

CALCULATION:

Given that u1 = 5m/s; u₂ = -1m/s (-ve due to opposite direction); v₁ = 0 m/s and v2 = ? and e = 1/3

We know that ​v2 − v1= − e (u2 − u1)

​v2 − (0) = − \( {1\over 3}\) (-1 − 5)

​v2 = −2 m/s (here -ve means opposite to initial direction)

So the correct answer is option 1.

Additional Information

• When e = 0, the balls remain in contact after the collision. (perfect inelastic collision)
• When e = 1, the collision is elastic.