Total distance travelled by a bouncing ball
Algebra
Level
3
A ball is dropped from a height of 1 metre bounces back to half its height. It keeps rebounding to half the height until it comes to rest. What is the total distance traveled by the ball before coming to rest
2.25
3
2
1.5
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The ball drops from 1 metre rebounds to half the height 0.5 metre once again drops 0.5 m and rebounds to 0.25 metre. This sequence continues until it comes to a stop.
S = 1 + 0.5 + 0.5 + 0.25 + 0.25 + 0.125 + 0.125....0
S = 1 + 1 + (0.5 + 0.25 + 0.125....)
The expression in brackets is an infinite GP with a = 0.5 and r = 0.5 so sum to infinite terms of a GP is a/1-r which is equal to 1.
S = 2 + 0.5/(1 - 0.5) = 3 metres.