Results 1 to 2 of 2

Math Help - Ant on Turntable

  1. #1
    Member billa's Avatar
    Joined
    Oct 2008
    Posts
    100

    Ant on Turntable

    " A turntable is spinning in the xy plane in a counterclockwise direction with a radius of 1 unit at a rotational velocity of 1 radian per second. A chord is drawn from (1,0) to (0,1) and an ant is placed at (1,0). The table begins to turn and the ant begins to walk at 1 unit per second with respect to the point he starts at.

    Find a parametric equation that gives the position of the ant at time t from t=0 to when the ant reaches the end of the chord. "

    I tried to write an equation to find the ant's position relative to the starting point, so I integrated the vector that describes the ant's direction. Then I added the vector that describes the position of the starting point. I got
    R = cos(t)+sin(3PI/4+t)-sin(3PI/4) i + sin(t) - cos(3PI/4+t)+cos(3PI/4)


    Unfortunately my book gives a much different answer


    Can anyone tell me what I did wrong?
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    The way I see it, if the turntable stayed stationary then at time t seconds the ant would reach the point \Bigl(1-\frac t{\sqrt2},\frac t{\sqrt2}\Bigr) on the line x+y=1. But in that time the turntable will actually have rotated through an angle t radians, so the ant will be at the point \Bigl(\Bigl(1-\frac t{\sqrt2}\Bigr)\cos t - \frac t{\sqrt2}\sin t, \Bigl(1-\frac t{\sqrt2}\Bigr)\sin t + \frac t{\sqrt2}\cos t\Bigr). It reaches the end of the chord at time t=\sqrt2, when it will be at the point (-\sin\sqrt2,\cos\sqrt2).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Parachutist landing on a turntable
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: December 22nd 2010, 12:08 PM
  2. Turntable - rotation?
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: May 21st 2009, 03:51 AM

Search Tags


/mathhelpforum @mathhelpforum