Explanation:
When the ball is dropped from a height of 10m, it gains potential energy due to its position above the ground. This potential energy is converted into kinetic energy as the ball falls towards the ground. However, when the ball impacts the ground, some of its energy is lost due to factors such as friction, heat, and sound.

In this case, there is a 40% loss of energy due to the impact. This means that only 60% of the initial energy is retained after the impact.

To calculate the height the ball will reach after one impact, we can use the principle of conservation of energy. The total mechanical energy (potential energy + kinetic energy) of the ball remains constant throughout the motion.

Let's assume the initial potential energy of the ball when it is at a height of 10m is E.

Calculations:
Initial potential energy (E) = mgh

Where:
m = mass of the ball (assuming it remains constant)
g = acceleration due to gravity (approx. 9.8 m/s²)
h = height of the ball (10m)

After the impact, the ball loses 40% of its energy. Therefore, the remaining energy is 60% of the initial energy.

Remaining energy after impact = 0.60 * E

This remaining energy is now converted into potential energy as the ball rebounds. Since the ball reaches its maximum height when it has only potential energy, we can equate the remaining energy to the potential energy at the maximum height.

Potential energy at maximum height = 0.60 * E

We can calculate the height using the potential energy formula:

Potential energy (PE) = mgh

Where:
m = mass of the ball (assuming it remains constant)
g = acceleration due to gravity (approx. 9.8 m/s²)
h = height of the ball (unknown)

0.60 * E = mgh

Now we can cancel out the mass (m) and acceleration due to gravity (g) from both sides of the equation:

0.60 * h = h

0.60 = h / h

0.60 = 1

Therefore, the height the ball will reach after one impact is equal to its initial height, which is 10m.

Answer:
The ball will go up to a height of 10m after one impact. Therefore, the correct choice is (a) 10m.

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