A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, their velocities after the collision will be, respectively

In an elastic collision, both momentum and kinetic energy are conserved. To determine the velocities of the two balls after the collision, we can use the following formulas for one-dimensional elastic collisions:

1. Velocity of the first ball after collision (v₁'):

   v₁' = [(m₁ - m₂) / (m₁ + m₂)] * u₁ + [(2 * m₂) / (m₁ + m₂)] * u₂

2. Velocity of the second ball after collision (v₂'):

   v₂' = [(2 * m₁) / (m₁ + m₂)] * u₁ + [(m₂ - m₁) / (m₁ + m₂)] * u₂

Where:

• m₁ and m₂ are the masses of the first and second balls, respectively.
• u₁ and u₂ are the initial velocities of the first and second balls, respectively.
• v₁' and v₂' are the velocities of the first and second balls after the collision, respectively.

Given:

• m₁ = 10 kg
• u₁ = 10 m/s
• m₂ = 5 kg
• u₂ = 4 m/s

Plugging in these values:

1. Calculating v₁':

   v₁' = [(10 kg - 5 kg) / (10 kg + 5 kg)] * 10 m/s + [(2 * 5 kg) / (10 kg + 5 kg)] * 4 m/s = (5 kg / 15 kg) * 10 m/s + (10 kg / 15 kg) * 4 m/s = (1/3) * 10 m/s + (2/3) * 4 m/s = 10/3 m/s + 8/3 m/s = 18/3 m/s = 6 m/s

2. Calculating v₂':

   v₂' = [(2 * 10 kg) / (10 kg + 5 kg)] * 10 m/s + [(5 kg - 10 kg) / (10 kg + 5 kg)] * 4 m/s = (20 kg / 15 kg) * 10 m/s + (-5 kg / 15 kg) * 4 m/s = (4/3) * 10 m/s - (1/3) * 4 m/s = 40/3 m/s - 4/3 m/s = 36/3 m/s = 12 m/s

Therefore, after the collision:

• The 10 kg ball will have a velocity of 6 m/s.
• The 5 kg ball will have a velocity of 12 m/s.