A mass of 4 kg is initially moving in the +x direction and collides inelastically with a mass of 8 kg moving in the -x direction at 7 m/s. After the collision, both masses move in the +x direction at 4 m/s. How fast was the 4 kg moving before the collision in m/s?

The initial velocity of 4 kg mass in positive 'x' direction is 26 m/s.

Explanation:

Consider the positive direction to have positive value and negative direction to have negative value.

Let the initial velocity of 4 kg mass be 'u' m/s in the positive 'x' direction.

Given:

Mass of body moving in positive direction is,

Mass of body moving in negative direction is,

Initial velocity of 8 kg mass is,

Combined velocity of the masses after collision is,

We know that, for an inelastic collision, the total momentum is conserved before and after collision. So,

Initial momentum of the masses = Final momentum of the masses

Now, plug in the given values and solve for 'u₁'. This gives,

Therefore, the initial velocity of 4 kg mass in positive x direction is 26 m/s.