How to Calculate Velocity After Elastic Collision?

Definition:

Elastic collision is used to find the final velocities v1^' and v2^' for the mass of moving objects m1 and m2.

Example:

Consider a moving object with the mass of 7kg with initial velocity of 4 ms^-1. The mass of the another moving object is 6kg. Find the after collision velocity v1^' and v2^' of the moving object?

Given:

Mass of Moving Object (m₁) = 7 kg Mass of Moving Object (m₂) = 6 kg Velocity of Stationary Object (v₁) = 4 ms^-1

Solution

v₁^' = ((m₁ - m₂) / (m₁ + m₂)) v₁ v₁^' = ((7 - 6) / (7 + 6)) x 4 v₁^' = (1 / 13) x 4 v₁^' = 0.307692308 v₂^' = (2m₁ / (m₁ + m₂)) v₁ v₂^' = ((2 x 7) / (7 + 6)) x 4 v₂^' = (14 / 13) x 4 v₂^' = 4.307692308