SOLUTION: Hi A ball drops from a height of 100m. each time it hits the ground, it bounces 60% of the height it fell. How far will the ball travel by the 4th bounce. Thanks

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Question 1205148: Hi
A ball drops from a height of 100m. each time it hits the ground, it bounces 60% of the height it fell. How far will the ball travel by the 4th bounce.
Thanks
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a ball drops from a height of 100m
Each time it hits the ground it bounces 60% of the height it fell. How far will it travel by the 4th bounce.
100m%2B+60m=160m.......bounces ones (60% of 100m is 60m )
60m%2B36m=96m.......bounces twice (60% of 60m is 0.6%2A60m=36m)
36m%2B21.6m=57.6m.......bounces three times (60% of 36m is 0.6%2A36m=21.6m)
21.6m%2B12.96m=34.56m.......bounces four times (60% of 21.6m is 0.6%2A21.6m=12.96m)
make table

# of+bounces|....Height fallen |.... Height+bounced |....+Distance+traveled |
|+1 |........................ 100m+............................+60m ................................. 160m+
| 2 |........................ .. 60m ........................ 36m........................ .... 96m+
|+3 | ........................ 36m ........................ 21.6m+........................ .. 57.6m
| 4+| ........................ 21.6m+........................ 12.96m ........................ 34.56m+

by the 4th bounce, the ball will have traveled a total distance of
160m+%2B+96m+%2B+57.6m+%2B+34.56m+=348.16m+

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
It's not at all clear what you mean by "by the 4th bounce".  

Here is the distance the ball has traveled, each time it
goes down then up. You decide when to stop.

1. Goes down 100m. The ball has traveled 100m.
Hits the ground the 1st time.

2. Goes up 60% of 100m, or 60m. The ball has traveled 160m.
3. Goes down 60m. The ball has traveled 220m.
Hits the ground the 2nd time.

4. Goes up 60% of 60m, or 36m. The ball has traveled 256m.
5. Goes down 36m. The ball has traveled 292m.
Hits the ground the 3rd time.

6. Goes up 60% of 36m, or 21.6m. The ball has traveled 313.6m.
7. Goes down 21.6m. The ball has traveled 335.2m.
Hits the ground the 4th time. 

8. Goes up 60% of 21.6m, or 12.96m. The ball has traveled 348.16m.
9. Goes down 12.6m. The ball has traveled 361.12m.
Hits the ground the 5th time.

When it hits the ground the 5th time it has traveled 361.12m 
If that's what you mean by "by the 4th bounce", that's the answer.
If you mean when it hits the ground the 4th time, the answer is 335.2m
If you mean when it rises to its highest point after hitting the ground
the 4th time, the answer is 313.6m.

Edwin