When analyzing collisions using the law of conservation of momentum, the same principles that allow us to analyze collisions in one dimension can also be used to analyze collisions in two dimensions. To do this, you must separately apply the law of conservation of momentum in the x- and y-directions. Use the following example to practice this process:

Two football players are about to collide with one another. Player 1 has a mass of 98.1 kg and is moving with a velocity of 4.52 m/s, 21.5° east of north. Player 2 has a mass of 79.4 kg and is moving with a velocity of 5.15 m/s, 8.55° east of south.

1. Find the x- and y-components of the momentum of each player.
2. What is the sum of the momenta in each dimension?
3. If, when the players collide, they hold onto each other and move as a single unit, what will be the velocity vector of that single unit?
4. Suppose that the two players collide, and bounce off each other. If player 2 is sent backwards with a velocity of 1.77 m/s, 15.5° west of north, what will be the velocity vector of payer 1 immediately after the collision.