Colliding body formula with new velocity

A classic physics problem!

The formula you're referring to is likely the equation for the velocity of one object after a collision with another object. This is often called the "coefficient of restitution" formula.

Let's assume we have two objects, A and B, with initial velocities vA and vB, respectively. After the collision, the velocities of the objects are vA' and vB'. The coefficient of restitution (e) is a dimensionless value that depends on the elasticity of the collision. It's defined as the ratio of the relative velocity after the collision to the relative velocity before the collision.

The formula for the velocity of object A after the collision is:

vA' = vA - e * (vA - vB)

And the formula for the velocity of object B after the collision is:

vB' = vB + e * (vA - vB)

Here, e is the coefficient of restitution, which is typically a value between 0 and 1. If e = 0, the collision is perfectly inelastic (the objects stick together), and if e = 1, the collision is perfectly elastic (the objects bounce off each other with the same velocity).

For example, if object A is moving at 10 m/s and object B is moving at 5 m/s, and the coefficient of restitution is 0.8, then after the collision:

vA' = 10 - 0.8 * (10 - 5) = 6 m/s vB' = 5 + 0.8 * (10 - 5) = 9 m/s

Note that these formulas assume a one-dimensional collision, where the objects are moving along the same line. In three-dimensional space, the collision is more complex and requires additional equations to describe the motion.