Question

A rubber ball is dropped from a height of 25 m, which strikes the ground and rebounds
everytimes to the half of the height from where it falls down. What is the total distance
travelled by the ball to come to the rest position.​

Answer 1

Answer: 49.90234375

Step-by-step explanation:

First we need to find out how many times 25 can be divided by 2 before we can get 0 in the whole number's place and the first decimal place.

25/2 = 12.5 - 1 time

12.5/2 = 6.25  - 2 times

6.25/2 = 3.125 - 3 times

3.125/2 = 1.5625 - 4 times

1.5625/2 = 0.78125 - 5 times

0.78125/2 = 0.390625 - 6 times

0.390625/2 = 0.1953125 - 7 times

0.1953125/2 = 0.09765625 - 8 times

So, the ball will stop bouncing after around 8 rebounds.

(We have not divided further after getting 0 in the whole number's place and the first decimal place as no number can be completely divided by any number which isn't its factor. So, since 2 is not a factor of 25 it cannot be fully divided but the division will go on infinitely. Also after the ball's energy is lowered to a certain amount, it will not bounce anymore, instead it will just directly  p a s s  all the energy into the ground in the last bounce, that is the bounce that will cause its energy to be lowered to the certain amount.)  

Now we have to add the distances travelled in each of those 8 bounces.

25 + 12.5 + 6.25 + 3.125 + 1.5625 + 0.78125 + 0.390625 + 0.1953125 + 0.09765625 = 49.90234375

Thus, the total distance travelled by the ball before coming to a rest is 49.90234375 m