The objects listed are placed at the top of a ramp and roll down to the bottom without slipping. Assuming that there is no air r
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The total momentum before and after the collision must be conserved.
The total momentum before the collision is:
where m1 and m2 are the masses of the two players, and
and 
their initial velocities. Both are considered with positive sign, because the two players are running toward the same direction.
The final momentum is instead
because now the two players are moving together with a total mass of (m1+m2) and final speed vf.
By requiring that the momentum is conserved
we can calculate vf, the post-collision speed:
and the direction is the same as the direction of the players before the collision.
The total momentum before the collision is:
where m1 and m2 are the masses of the two players, and
The final momentum is instead
because now the two players are moving together with a total mass of (m1+m2) and final speed vf.
By requiring that the momentum is conserved
we can calculate vf, the post-collision speed:
and the direction is the same as the direction of the players before the collision.