Explanation:
When a ball is allowed to fall from a height of 20 m, it loses 40% of its energy due to impact. This means that the ball will not rebound to the same height from which it was dropped. Let's calculate the height to which the ball will rebound.

Step 1: Calculate the potential energy of the ball at the top of its fall.

Potential energy (PE) = mgh
where m = mass of the ball, g = acceleration due to gravity, and h = height

Let's assume the mass of the ball is 1 kg. The acceleration due to gravity is 9.8 m/s^2. Therefore, the potential energy of the ball at the top of its fall is:

PE = 1 kg x 9.8 m/s^2 x 20 m = 196 J

Step 2: Calculate the kinetic energy of the ball just before impact.

At the point of impact, all the potential energy of the ball is converted into kinetic energy. Therefore, the kinetic energy just before impact is:

KE = 1/2 mv^2
where v = velocity of the ball just before impact

Since the ball is falling freely, we can use the equation of motion:

v^2 = u^2 + 2gh
where u = initial velocity (which is zero because the ball is dropped from rest), g = acceleration due to gravity, and h = height

Substituting the values, we get:

v^2 = 0 + 2 x 9.8 m/s^2 x 20 m = 392
v = √392 = 19.8 m/s

Therefore, the kinetic energy just before impact is:

KE = 1/2 x 1 kg x (19.8 m/s)^2 = 196 J

Step 3: Calculate the energy lost due to impact.

According to the problem, 40% of the energy is lost due to impact. Therefore, the energy remaining after impact is:

ER = KE x (100% - 40%) = KE x 60% = 0.6 x 196 J = 117.6 J

Step 4: Calculate the height to which the ball will rebound.

The remaining energy is converted into potential energy as the ball rebounds. Therefore, we can use the formula:

PE = mgh
where m = mass of the ball, g = acceleration due to gravity, and h = height

Substituting the values, we get:

117.6 J = 1 kg x 9.8 m/s^2 x h
h = 117.6 J / (1 kg x 9.8 m/s^2) = 12 m

Therefore, the ball will rebound to a height of 12 m.

At 20m ball's energy will be m×10×20=200m jouleslost energy=80m joulesso, energy after impact = 200m - 80m=120m.at last,120 m joules= m× 10×h:h=12 metres.