## Introduction

The coefficient of restitution is a fundamental concept in physics and mechanics that measures the ratio of velocities before and after a collision between two objects. It is a crucial parameter in understanding the kinetic energy transfer during collisions.

## Definition

The coefficient of restitution, denoted as e, is defined as the ratio of the relative velocity of separation and the relative velocity of approach of two objects during a collision.

## Formula

The formula for calculating the coefficient of restitution is: e = (v2f – v1f) / (v1i – v2i), where v1i and v2i are the initial velocities of the two objects, and v1f and v2f are their final velocities.

## Importance

The coefficient of restitution helps determine whether a collision is elastic (e = 1), inelastic (0 < e < 1), or completely inelastic (e = 0). It provides valuable information on how much kinetic energy is conserved during a collision.

## Examples

- An example of a perfectly elastic collision is two billiard balls striking each other, where no kinetic energy is lost.
- A common example of an inelastic collision is a car crash, where some kinetic energy is converted into other forms like heat and sound.

## Case Studies

In sports like basketball and volleyball, understanding the coefficient of restitution helps players predict the trajectory of the ball after a bounce, enabling better coordination and gameplay.

## Statistics

Studies have shown that the coefficient of restitution plays a crucial role in designing efficient energy-absorbing materials for car bumpers and sports equipment to minimize injuries during collisions.