[Guest]

A ball is dropped from a distance of 11m.

Each time, it bounces back to a height which is half of the previous one.

What is the total distance travelled by the ball when it comes to rest.

[Guest]

33

I guess it's gotta be 33. Our equation is 11 + 2*11/2 + 2*11/4 + 2*11/8 ... etc which equals 11 + 2*Sum(11/2^n) for values of n from 1 to infinity.

That simplifies to 11 + 22*Sum(1/2^n). As n approaches infinity, Sum(1/2^n) approaches 1.

Therefore the distance is approximately 11 + 22*1 = 33.

Right. Got it.

So the ball falls, bounces and travels 33 metres before coming to rest.

Right?

Yes guys, you all got it.

I have written a small program in C to illustrate the situation (see attachment).

It is evident from the program that generally, if it is dropped from a distance of x meters, it would travel a distance of 3x.

The source code of the program is as follows:

#include<stdio.h>

#include<conio.h>

int main()

{

float i,j,sum;

printf("Ball is dropped from a distance of : ");

scanf("%f",&j);

sum=j;

while(j!=0)

{

sum=sum+2*(j/2);

j=j/2;

}

printf("\nApproximate total distance travelled = %0.0f",sum);

getch();

return 0;

}

Bouncing_Ball.zip