A98-kg fullback is running along at 8.6 m / s when a 76-kg defensive back running in the same direction at 9.8 m / s jumps on his back. what is the post-collision speed of the two players immediately after the tackle

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.