Two football players collide head-on in midair while chasing a pass. The first player has a 110 kg mass and an initial velocity of 4.40 m/s in the positive x direction, while the second player has a 135 kg mass and initial velocity of 3.30 m/s in the negative x direction. Required:
What is the x component of their velocity just after impact if they cling together?

v = 0.16 m/s in the positive x direction.

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved.Initial momentum can be expressed as follows:

       

Since both players move only horizontally, (1) can be expressed in terms of the velocities in the x- directions only, taking into account that player 1 moves in the positive x-direction, and player 2 in the opposite direction, and assuming that positive velocities are in the positive x-direction also:

       

Since total momentum must be conserved, the final momentum must be equal to the initial one.We know that both players cling together after colliding, so the collision is totally inelastic.So, the final momentum can be expressed as follows:

       

Replacing by the givens in (3), we get:

       

Since (3) must be equal to (4) we can solve for vf, as follows:

       

Since the initial momentum has only component in the x-direction, the final one must have component in the x-direction only too.This means that vf is in the x-direction, and due to it is positive, it must aim in the positive x-direction.So, vfx = +0.16 m/s

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