after striking the floor a ball rebounds 4/5th of the height from which it has fallen find the total distance travelled before coming to rest considering its dropped from 100m
To find the total distance traveled by the ball before coming to rest, we need to consider the distances traveled during each bounce. Let's break it down step by step:
Step 1: Calculate the distance traveled during the first bounce.
After the ball is dropped from a height of 100m, it rebounds 4/5th of the height. Therefore, during the first bounce, the ball reaches a height of (4/5) * 100m = 80m.
Step 2: Calculate the distance traveled during the second bounce.
During the second bounce, the ball starts from a height of 80m and rebounds again to 4/5th of that height. Thus, the height of the second bounce is (4/5) * 80m = 64m.
Step 3: Calculate the distance traveled during the third bounce.
During the third bounce, the ball starts from a height of 64m and rebounds to 4/5th of that height. Therefore, the height of the third bounce is (4/5) * 64m = 51.2m.
We can observe that with each bounce, the height decreases. Eventually, the height will become so small that it can be considered negligible. At this point, the ball will come to rest, as it won't bounce anymore.
So, the total distance traveled by the ball before coming to rest can be calculated by adding the distances traveled during each bounce.
Total distance = 100m + 80m + 64m + 51.2m + ...
To find the exact total distance, we can represent the pattern using a geometric series:
S = a / (1 - r)
Where:
S is the sum of the series,
a is the first term,
r is the common ratio.
In this case, a = 100m and r = 4/5.
S = 100m / (1 - 4/5)
S = 100m / (1/5)
S = 500m
Therefore, the total distance traveled by the ball before coming to rest is 500m.