The total distance travelled by the particle before it stops can be calculated using the concept of the coefficient of restitution. The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in a collision. In this case, it represents the ratio of the final to initial relative velocity between two objects after they collide.

When the particle falls from a height 'h', it hits the ground and rebounds to a height of 'eh'. This is because the velocity with which it rebounds is 'e' times the velocity with which it hit the ground.

The particle will continue to rebound, each time reaching a height of 'e' times the previous height. This forms a geometric progression with the first term as 'h' and the common ratio as 'e'.

The total distance travelled by the particle is the sum of the distances travelled in each bounce. This forms an infinite geometric series, the sum (S) of which can be calculated using the formula:

S = a / (1 - r)

where 'a' is the first term and 'r' is the common ratio.

Substituting 'h' for 'a' and 'e' for 'r', we get:

S = h / (1 - e)

This is the total distance travelled by the particle before it stops.

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The total distance travelled by the particle before it stops can be calculated using the concept of the coefficient of restitution. The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in a collision. In this case, it represents the ratio of the final to initial relative velocity between two objects after they collide.

When the particle falls from a height 'h', it hits the ground and rebounds to a height of 'eh'. This is because the velocity with which it rebounds is 'e' times the velocity with which it hit the ground.

The particle will continue to rebound, each time reaching a height of 'e' times the previous height. This forms a geometric progression with the first term as 'h' and the common ratio as 'e'.

The total distance travelled by the particle is the sum of the distances travelled in each bounce. This forms an infinite geometric series, the sum (S) of which can be calculated using the formula:

S = a / (1 - r)

where 'a' is the first term and 'r' is the common ratio.

Substituting 'h' for 'a' and 'e' for 'r', we get:

S = h / (1 - e)

This is the total distance travelled by the particle before it stops.

Knowee AI · Accepted Answer

The total distance travelled by the particle before it stops can be calculated using the concept of the coefficient of restitution. The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in a collision. In this case, it represents the ratio of the final to initial relative velocity between two objects after they collide.

When the particle falls from a height 'h', it hits the ground and rebounds to a height of 'eh'. This is because the velocity with which it rebounds is 'e' times the velocity with which it hit the ground.

The particle will continue to rebound, each time reaching a height of 'e' times the previous height. This forms a geometric progression with the first term as 'h' and the common ratio as 'e'.

The total distance travelled by the particle is the sum of the distances travelled in each bounce. This forms an infinite geometric series, the sum (S) of which can be calculated using the formula:

S = a / (1 - r)

where 'a' is the first term and 'r' is the common ratio.

Substituting 'h' for 'a' and 'e' for 'r', we get:

S = h / (1 - e)

This is the total distance travelled by the particle before it stops.

particle falls from a height 'h' on a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution, the total distance travelled by the particle before it stops is

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