According to the law of conservation of momentum, the total momentum of a system remains constant if there are no external forces acting on the system. In this case, the system consists of the person on roller skates and the ball that is thrown.
Before the collision, the ball has momentum, and the person on roller skates is stationary. After the collision, both the ball and the person on roller skates have momentum, and they move together in the same direction.
Since the momentum of the system is conserved, the total momentum before the collision must be equal to the total momentum after the collision. Therefore, the momentum of the ball before the collision is equal to the momentum of the ball and the person on roller skates after the collision.
If we assume that the person on roller skates is much more massive than the ball, then the momentum of the person on roller skates can be neglected. In this case, the momentum of the ball before the collision is equal to the momentum of the ball and the person on roller skates after the collision.
Since the mass of the ball is much smaller than the combined mass of the ball and the person on roller skates, the speed of the ball after the collision will be much smaller than its speed before the collision. Meanwhile, the speed of the person on roller skates after the collision will be faster than their initial stationary position due to the transfer of momentum from the ball to the person on roller skates.
In summary, the speed of the ball after the collision will be slower than its initial speed, while the speed of the person on roller skates will be faster than their initial stationary position.
~~~Harsha~~~