A 4kg and 5kg bodies moving on a frictionless horizontal surface at a velocity of ( -6i )m/s and ( +3 )m/s respectively. Collide a head on elastic collision. What is the velocity ( magnitude and direction) of the each body after collision?

4 kg → +4 m/s

5 kg → -5 m/s

Explanation:

The law of conservation of momentum states that:

You'll notice that we have two missing variables: v₁' & v₂'. Assuming this is a perfectly elastic collision, we can use the conservation of kinetic energy to set the initial and final velocities of the individual bodies equal to each other.

Let's substitute all known variables into the first equation.

Let's substitute the known variables into the second equation.

Now we have a system of equations where we can solve for v₁ and v₂.

Use the elimination method and multiply the bottom equation by -4.

Add the equations together.

The final velocity of the second body (5 kg) is -5 m/s. Substitute this value into one of the equations in the system to find v₁.  

The final velocity of the first body (4 kg) is 4 m/s.

We can verify our answer by making sure that the law of conservation of momentum is followed.

The combined momentum of the bodies before the collision is equal to the combined momentum of the bodies after the collision. [✓]