A rubber ball is dropped from a certain height. After striking the floor, the ball bounces to 3/4th of the height it was dropped from. If the ball is initially dropped from a heigh of 100 meters, what is the total distance travelled by the ball before it comes to rest?

To find the total distance traveled by the ball before it comes to rest, we need to consider the distance it travels during each bounce.

1. The ball is initially dropped from a height of 100 meters.
2. It strikes the floor and bounces back up to 3/4th of the height it was dropped from, which is 3/4 * 100 = 75 meters.
3. The ball then falls back down to the floor and bounces up again, reaching a height of 3/4 * 75 = 56.25 meters.
4. This process continues, with each bounce reaching a height that is 3/4th of the previous bounce's height.
5. We can calculate the total distance traveled by summing up the distances traveled during each bounce.

Let's calculate the distances for each bounce:

Bounce 1: Distance traveled = 100 + 75 = 175 meters Bounce 2: Distance traveled = 75 + 56.25 = 131.25 meters Bounce 3: Distance traveled = 56.25 + 42.19 = 98.44 meters Bounce 4: Distance traveled = 42.19 + 31.64 = 73.83 meters Bounce 5: Distance traveled = 31.64 + 23.73 = 55.37 meters Bounce 6: Distance traveled = 23.73 + 17.80 = 41.53 meters Bounce 7: Distance traveled = 17.80 + 13.35 = 31.15 meters Bounce 8: Distance traveled = 13.35 + 10.01 = 23.36 meters Bounce 9: Distance traveled = 10.01 + 7.51 = 17.52 meters Bounce 10: Distance traveled = 7.51 + 5.63 = 13.14 meters

To find the total distance traveled, we add up all the distances:

Total distance traveled = 175 + 131.25 + 98.44 + 73.83 + 55.37 + 41.53 + 31.15 + 23.36 + 17.52 + 13.14 = 660.59 meters

Therefore, the total distance traveled by the ball before it comes to rest is 660.59 meters.