Posted by **Fidelia** on Thursday, May 31, 2007 at 9:23pm.

5. A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface the fifth time?

The answer is 54 and 21/125 ft, but why?

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface the fifth time?

Dwn.Up.Dwn.Up.Dwn..Up...Dwn...Up...Dwn

15..9...9.5.4.5.4.3.24.3.24.1.944.1.944

Ssumming yields 54.168 = 54 21/125 feet.

- math -
**Ria Rana**, Sunday, April 24, 2011 at 8:11pm
Guys, here is the answer.

Ball is dropped from a height of 15 feet and each bounce it goes to 3/5 as high as the preceding one.

Now, total distance traveled in:

1st drop:15 (till it hits the ground)

2nd drop:(15*3/5)=9*2=18 [Multiply by 2 as distance to go up (15*3/5) and to come down (15*3/5),so multiply by 2]

3rd drop: (9*3/5)=5.4*2 =10.8

4th drop: (5.4*3/5)=3.24*2 =6.48

5th drop: (3.24*3/5)=1.94*2= 3.888 (now ball will hit the ground after 5th fall)

total distance: distance in 1st drop+ 2nd drop+3rd drop+4th drop+5th drop.

= 15+18+10.8+6.48+3.888=54.168

Hope this helps....

- math -
**Gince Mungs**, Sunday, May 5, 2013 at 4:15am
It's a sort og geometric series with limiting sum. Please I need a perfect formula to calculate it instead of the normal addition

- math -
**Anonymous**, Monday, December 9, 2013 at 7:31pm
each time a bouncy ball bounce, it bounces to half the height from which it had just fallen. if jack drops a ball from a building and it rises to a height of 24 metres, how high will it bounce on the fifth bounce?

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