Physics Question on laws of motion

Question

A ball falls freely from a height h on a rigid horizontal plane. If the coefficient of resolution is e, then the total distance travelled by the ball before hitting the plane second time is:

Answer 1

Solution

The correct option is: (B) : h(1+2e2).

Prior to the initial collision, the following relationship exists:

mgh = (1/2)mv₁²

This can be further expressed as:

v₁ = √(2gh)

Following the collision, the velocity becomes v₂. Hence, the relationship can be described as:

v₁/v₂ = e Or, v₂ = ev₁

Considering the subsequent calculation of the ball's reached height:

mgh₂ = (1/2)mv₂²

This leads to the equation:

h₂ = (1/2)e²h

The total distance covered before the second impact is determined by:

h + (1/2)h₂ = h + (1/2)e²h = h(1 + 2e²)