Momentum and Impulse in 2D

Conservation of momentum applies to two dimensions just like in one dimension; the total momentum before an event (e.g., collision or explosion) is equal to the total momentum after the event, provided no external forces are involved.
Vector quantities should be broken down into their components along the x and y axes to simplify calculations.

Both elastic and inelastic collisions can involve two-dimensional scenarios; be prepared to apply the principles of each type of collision in two dimensions.
Oblique collisions involve objects colliding at an angle. You’ll need to use trigonometry to resolve such problems, breaking down velocities and forces into their components.

Impulse is a vector quantity, akin to momentum. When calculating impulse in two dimensions, apply the same principle of breaking down vector quantities into their x and y components.
Impulse in 2D can be calculated by the product of force and change in time in each direction separately.

The coefficient of restitution still applies to 2D problems. It is calculated in the same way, regardless of the number of dimensions, as the ratio of relative velocity of separation to the relative velocity of approach.

Force-time graphs can be used to find the impulse delivered in each direction. The area under the graph in each direction represents the total impulse.

Often, a problem involving momentum and impulse in two dimensions can be made simpler by analysing each direction separately, then combining the results at the end.
Trigonometry is key tool for resolving vector quantities into their components. Always consider using trigonometric rules when facing angled collisions, forces, or velocities.
Remember to use sketches to help visualise the problem and to keep track of the various forces, velocities, and directions involved.