Results 1 to 3 of 3

Thread: Parabola for Golf Ball Roll on Green

  1. #1
    Jun 2010

    Parabola for Golf Ball Roll on Green


    I'm having a hard time coming up with a formula for showing how a golf ball will "roll" on a sloped green.

    For example, assume there is a right to left break of 1 degree and the ball is hit straight. The ball will end up on a path that is exactly 10 degrees to the left of the hole.

    I need a formula so that the line will start at the center of the golf ball and pass through a point 10 degrees left of the hole (with a curve, not a straight line)

    Any help is appreciated.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member slider142's Avatar
    May 2009
    Brooklyn, NY
    Do you wish to include friction? A frictionless analysis gives a parabola whose curvature depends on the ball's initial velocity and the degree of the slope.
    Specifically, if we let the Cartesian plane be the plane that is sloped 1 degree (pi/180 radians) from the positive y-axis to the negative y-axis, and we hit the ball along the negative x-axis from the origin, the ball will describe the path
    $\displaystyle y = -\left(\frac{g\sin\left(\frac{\pi}{180}\right)}{2v^ 2}\right)x^2$
    g is the acceleration due to gravity where the green is located. At sea level, it is usually 9.8 meters/(second^2). v is the initial velocity with which the ball is hit along the negative x-axis. You will need to find the correct v to deviate from the hole in the correct way:
    If the hole is located at (-R, 0), then you must solve the equation
    $\displaystyle R = \frac{2v^2\tan\left(\frac{\pi}{18}\right)}{g\sin\l eft(\frac{\pi}{180}\right)}$
    to get the initial velocity v necessary to accomplish your deviation of 10 degrees (pi/18 radians).
    If you simply want the curve and you don't actually care about v, simply replace v with the relevant function of R in the original equation:
    $\displaystyle y = -\left(\frac{\tan\left(\frac{\pi}{180}\right)}{R}\r ight)x^2$
    If you want to include non-zero friction, the result is a solution of a differential equation that is no longer a parabola.
    Last edited by slider142; Jun 24th 2010 at 04:01 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Jun 2010
    Thank you very much...I'm going to try this in my graphing tool.

    I really appreciate the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Nov 9th 2010, 12:01 AM
  2. linear map open iff image of unit ball contains ball around 0
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 25th 2010, 01:15 AM
  3. Replies: 2
    Last Post: Dec 9th 2008, 01:55 AM
  4. parabola ball
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Sep 5th 2008, 07:20 PM
  5. A golf ball traveling 3 m/s
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: Aug 16th 2006, 11:42 AM

Search Tags

/mathhelpforum @mathhelpforum