Question

The height of office from the ground is 12 meters. A ball falls down from the top and bounces half the distance back each time. It stops after 6 bounces. What is the total travelling distance of the ball?

Answer 1

1st bounce distance travelled =12+6=18m

2nd will be 6+3=9m

3rd   3+1.5=4.5m

4th   1.5+0.75=2.25m

5th   0.75+0.375=1.125m

6th   0.375+0.1875=0.5625m

Ball is in the air now so it comes 0.5625m down and stops.

total distance travelled =18+9+4.5+2.25+1.125+0.5625+0.5625=36m

Comments

36m is the distance it would have moved if allowed to continue to bounce indefinitely (theoretically).

Answer 2

The ball drops 12m before the first bounce.

The subsequent bounces take the ball to 6m, then, 3m, etc. So the total distance is:

12+2(6+3+...) which can be written:

12+2×6(1+½+¼+...).

We have a geometric series with 6 terms:

12+12(1-(1/2⁶))/(1-½)=12+24(63/64)=12+⅜×63=

12+189/8=12+23⅝=35⅝=35.625m.