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# How high will the ball bounce?

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.
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naseeam
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2 Solutions

Commented:
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.
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Commented:
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
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Commented:
There is no absolute answer but 4.56 m is a good estimate.
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Commented:
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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Commented:
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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Commented:
..if you take the ratio as approximately .74 then

h/6 = .74

Which gives h as

h = 4.44
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Commented:
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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