A0.25kg rubber ball is released from a height of 10m and is allowed to bounce repeatedly.

The maximum height the ball will reach after hitting the ground four times = 5.84 m

Explanation:

Kinetic Energy: This is the energy of a body, by virtue of its motion. The S.I unit of kinetic Energy is Joules(J).

At the point when the ball hits the ground, the kinetic energy is converted to potential energy.

Ep = mgh Equation 1

Where E p = potential Energy, m = mass of the ball, g = acceleration due to gravity, h = height.

Given: m = 0.25 kg, h = 10 m,

Constant: g = 9.81 m/s²

Substituting into equation 1,

Ep = 0.25(10)(9.81)

Ep = 24.525 J.

Each time the ball hits the ground, 10 percent of the ball's kinetic energy is lost  in the collision.

The ball will lost 40 percent of its energy after hitting the ground four times.

Energy lost after hitting the ground four times = 24.525(0.4) =  10.21 J.

Ep₁ = 24.525 - 10.21

Ep₁ = 14.315 J.

Where Ep₁ = Energy of the ball after hitting the ground four times.

But

h = Ep₁/mg Equation 2

h = 14.315/(0.25×9.81)

h = 14.315/2.4525

h =  5.84 m.

Thus the maximum height the ball will reach after hitting the ground four times = 5.84 m

The vertical axis represents the velocity of the object. This probably sounds obvious, but be forewarned—velocity graphs are notoriously difficult to interpret. People get so used to finding velocity by determining the slope—as would be done with a position graph—they forget that for velocity graphs the value of the vertical axis is giving the velocity.

Try sliding the dot horizontally on the example graph below to choose different times and see how the velocity changes.

Explanation: