Describe an elastic collision.

An elastic collision is a collision where both kinetic energy and momentum are conserved.

In an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision. This means that the objects involved in the collision bounce off each other without any loss of energy due to deformation or friction.

Mathematically, we can express the conservation of momentum and kinetic energy as follows:

Conservation of momentum:
m1v1i + m2v2i = m1v1f + m2v2f

where m1 and m2 are the masses of the objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.

Conservation of kinetic energy:
(1/2)m1v1i^2 + (1/2)m2v2i^2 = (1/2)m1v1f^2 + (1/2)m2v2f^2

where the terms on the left-hand side represent the initial kinetic energy of the system, and the terms on the right-hand side represent the final kinetic energy of the system.

Solving these equations simultaneously will give us the final velocities of the objects after the collision.

Overall, elastic collisions are important in physics because they allow us to study the behaviour of objects without the complicating factors of energy loss or deformation.