We are given that a ball is dropped from a height h1 of 1200mm and the coefficient of restitution (COR) is 0.8. We need to find the height h5 of the ball after its 5th rebound from a horizontal floor.


The coefficient of restitution (COR) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the final relative velocity of separation to the initial relative velocity of approach between the objects. In simpler terms, it represents how bouncy an object is.


When the ball is dropped from a height h1, it will rebound after hitting the floor. Let's denote the height of the 1st rebound as h2.

Using the coefficient of restitution, we can calculate the relative velocity of separation after the collision as v2 = COR * v1, where v1 is the relative velocity of approach before the collision.

Since the ball is dropped, the initial relative velocity of approach is equal to the initial velocity of the ball just before it hits the floor, which can be calculated using the equation v1 = sqrt(2 * g * h1), where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Now, we can calculate the height of the 1st rebound using the equation h2 = (v2^2) / (2 * g).


Once we have calculated the height of the 1st rebound, we can repeat the process to find the heights of the 2nd, 3rd, 4th, and 5th rebounds.

For each rebound, we need to calculate the relative velocity of approach v1 using the equation v1 = sqrt(2 * g * h), where h is the height of the previous rebound.

Then, we can calculate the relative velocity of separation v2 using v2 = COR * v1.

Finally, we can calculate the height of the next rebound using the equation h = (v2^2) / (2 * g).


By repeating the above steps, we can calculate the heights of the 2nd, 3rd, 4th, and 5th rebounds. The height of the 5th rebound will be denoted as h5.


To find the height of the 5th rebound of a ball dropped from a height h1 with a coefficient of restitution of 0.8, we need to calculate the heights of the 1st to 4th rebounds using the equations mentioned above. The height of the 5th rebound can then be determined.