How high will the ball bounce?

Posted on 2012-09-03
Last Modified: 2012-09-03
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.
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.
    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
    LVL 17

    Expert Comment

    There is no absolute answer but 4.56 m is a good estimate.
    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
    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.
    LVL 31

    Expert Comment

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

    h/6 = .74

    Which gives h as

    h = 4.44
    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.

    Write Comment

    Please enter a first name

    Please enter a last name

    We will never share this with anyone.

    Featured Post

    How your wiki can always stay up-to-date

    Quip doubles as a “living” wiki and a project management tool that evolves with your organization. As you finish projects in Quip, the work remains, easily accessible to all team members, new and old.
    - Increase transparency
    - Onboard new hires faster
    - Access from mobile/offline

    Suggested Solutions

    Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
    Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
    This video gives you a great overview about bandwidth monitoring with SNMP and WMI with our network monitoring solution PRTG Network Monitor ( If you're looking for how to monitor bandwidth using netflow or packet s…
    Polish reports in Access so they look terrific. Take yourself to another level. Equations, Back Color, Alternate Back Color. Write easy VBA Code. Tighten space to use less pages. Launch report from a menu, considering criteria only when it is filled…

    737 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    22 Experts available now in Live!

    Get 1:1 Help Now