Collisions in Multiple Dimensions: Problem Solving

In a two-dimensional collision, momentum is conserved in the x and the y-direction independently.

For example, two skiers collide at an icy intersection and get stuck with each other. What will be the velocity of the skiers and their direction of travel after collision?

The two skiers form a closed system. In this case, as the skiers intersect at right angles, we assume the positive x-axis along the direction of the first skier and the positive y-axis along the direction of the second skier.

If the mass and velocity of the skiers before collision are known, then the velocity and direction of the skiers after collision can be resolved.

The equations for momentum conservation in the x and y direction are stated independently to resolve for the final momentum components.

The magnitude of the final momentum vector is obtained using the Pythagorean theorem from which the velocity of the skiers is obtained.

The direction of the skiers after the collision is obtained using the inverse tangent function for the momentum components.