The distance traveled by a body before it comes to rest after falling from a height on the ground is determined by the coefficient of restitution (e).

Definition of Coefficient of Restitution:
The coefficient of restitution (e) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.

Explanation:

Step 1: Understanding the Initial Conditions
When the body falls from a height (h) on the ground, it possesses potential energy (mgh) which is converted into kinetic energy as it falls. The initial velocity (u) of the body just before collision with the ground can be determined using the equation:
mgh = (1/2)mu²

where,
m = mass of the body
g = acceleration due to gravity (9.8 m/s²)
h = height of fall
u = initial velocity of the body just before collision

Step 2: Collision with the Ground
When the body collides with the ground, the collision is not perfectly elastic, and some energy is lost. The coefficient of restitution (e) determines the amount of energy retained after the collision. It is given by the equation:
e = (v - u) / (u - 0)

where,
v = final velocity of the body just after collision

Step 3: Determining the Final Velocity
The final velocity (v) of the body just after the collision can be determined using the equation:
v = eu

Step 4: Time of Flight
The time taken by the body to reach the ground from height (h) can be determined using the equation:
h = (1/2)gt²

where,
t = time of flight

Step 5: Distance Traveled before Coming to Rest
The distance traveled by the body before it comes to rest can be determined by multiplying the time of flight (t) by the final velocity (v).
Distance = v * t

Summary:
In summary, the distance traveled by a body before it comes to rest after falling from a height on the ground can be determined by finding the initial velocity (u), final velocity (v), and time of flight (t). The coefficient of restitution (e) plays a crucial role in determining the final velocity of the body after collision with the ground. The distance traveled can be calculated by multiplying the final velocity with the time of flight.

H/(1-e^2) ?