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# How high will the ball bounce?

Posted on 2012-09-03
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As part of a science experiment, you drop a ball from various heights and measure how high it bounces on the first bounce.  The results of six drops are given below.

Drop height (m)                           0.5      1.5       2          2.5       4           5
First bounce height (m)              0.38     1.15    1.44     1.90     2.88      3.85

How high will the ball bounce if you drop it from a height of 6 meters?

Is there a pattern here?  I couldn't find a pattern.

This is high school Algebra 2 problem.  It's not homework.
0
Question by:naseeam

LVL 17

Accepted Solution

4.56 m

.38 x 1 or .5m = .38m
.38 x 10 or 5m = 3.8m
.38 x 12 or6m = 4.56 m

There are some factors that I can not calculate.
But I hope this help somewhat.
0

LVL 11

Expert Comment

I guess you could start by calculating the velocity of the ball when it hits by using the formula

v = sqrt(2gy))

Then you could calculate the efficiency of the ball by how high it bounces back.  It seems to be about 75% efficient
0

LVL 17

Expert Comment

There is no absolute answer but 4.56 m is a good estimate.
0

LVL 31

Assisted Solution

The ratios of the all the heights are the same

0.38/0.5 = .76

1.15/1.115 = .74

1.44/2 = .72

1.9/2.5= .76

2.88/4 = .72

The data is to with in experimental error approximated by a straight line, (which analytically the ball should do). My guess is the problem is to find the best fit through this data
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LVL 11

Expert Comment

LOL, ok, no need to calculate the velocity, it is just the ratio of how high the ball bounces compared to where it was dropped from.
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LVL 31

Expert Comment

..if you take the ratio as approximately .74 then

h/6 = .74

Which gives h as

h = 4.44
0

LVL 19

Expert Comment

Theory may predict a perfect straight line, but as others have mentioned here, expect some error.  Welcome to the real world!  This real deviation from theory is one of the more challenging parts of science.
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