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Collisions in two dimensions
Intermediate
Conserve momentum separately along each axis.
Conserve momentum separately along x and y. With an unknown number of unknowns, you usually need extra info (angles) or energy conservation.
A ball hits a stationary one and goes off at 30°; use the components to find the other's direction.
Momentum is a vector; don't use the magnitudes.
In more detail
In two-dimensional collisions, momentum is conserved along each axis separately. Combined with energy conservation for elastic collisions, the final velocities can be found.
Real-world uses
- Analysing pool ball collisions at angles.
- Accident reconstruction uses 2D momentum analysis for vehicles that collide at junctions.
- Pool players use two-dimensional momentum conservation to predict where a ball goes after it strikes another at an angle.
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Frequently asked questions
Do I apply conservation along each axis?
Yes. Momentum components along x and y are each conserved in an isolated collision.
What information do I need?
Usually the masses, initial velocities and one direction or angle after the collision.
What is conserved in a two-dimensional collision?
Total momentum in each direction separately, and kinetic energy in the elastic case.
Related topics in Momentum & Collisions
Heavy hits light object · Energy lost in inelastic collision · Reduced mass · Billiard ball collisions · Ballistic pendulum · Bouncing ball