A golf ball, dropped from 2 meters above a floor, rebounds to a height of 1.6 meters. What percentage of its energy of motion is lost in the collision with the floor?

To find the percentage of energy lost in the collision, we first need to calculate the initial and final energies of the golf ball.

The initial energy, also known as the potential energy, is given by the equation:

E_initial = m * g * h_initial

where m is the mass of the golf ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h_initial is the initial height from which the ball was dropped.

The final energy, also known as the potential energy at the rebound height, is given by:

E_final = m * g * h_final

where h_final is the height to which the ball rebounds.

In this case, the initial height (h_initial) is 2 meters and the rebound height (h_final) is 1.6 meters.

So, we can calculate the initial and final energies using the given information.

E_initial = m * g * h_initial
E_initial = m * 9.8 * 2
E_initial = 19.6 * m

E_final = m * g * h_final
E_final = m * 9.8 * 1.6
E_final = 15.68 * m

The energy lost in the collision can be calculated as the difference between the initial and final energies:

E_lost = E_initial - E_final
E_lost = 19.6 * m - 15.68 * m
E_lost = 3.92 * m

To find the percentage of energy lost, we need to compare the energy lost (E_lost) with the initial energy.

Percentage of energy lost = (E_lost / E_initial) * 100

Substituting the values, we get:

Percentage of energy lost = (3.92 * m) / (19.6 * m) * 100
Percentage of energy lost = 3.92 / 19.6 * 100
Percentage of energy lost = 20%

Therefore, the golf ball loses 20% of its energy of motion in the collision with the floor.