Results 1 to 1 of 1

Math Help - Polar coords and differentiation

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    1

    Polar coords and differentiation

    Hey guys, got a polar coordinates question Im stuck on.

    A particle is moving with constant velocity \vec{v} = u\hat{i} along the line y = 2. Describe \vec{v} in polar coordinates.

    I worked out that r_t = \sqrt{(vt)^2 + 4} and differentiating that shouldnt be too much of a problem but Im stuck with theta

    Ive got \theta_t = \arctan\frac{y}{x} = \arctan\frac{2}{vt}
    but Im guessing I cant just differentiate this using \frac{d}{dx} arctan(x) = \frac{1}{x^2 + 1}, since theres \frac{1}{t} in there instead of t.

    I worked through it using \frac{d\theta}{dt} = \frac{1}{\frac{dt}{d\theta}} and ended up with

    \displaystyle{\frac{d\theta}{dt}}=\frac{1}{\frac{d  }{d\theta}(\frac{2}{\vec{v}}\frac{1}{tan\theta})}=  \frac{1}{-\frac{2}{\vec{v}}\frac{sec^2\theta}{tan^2\theta}}

    \frac{d\theta}{dt}=-\frac{\vec{v}tan^2\theta}{2sec^2\theta}=-\frac{\vec{v}}{2}\tan^2(\theta)cos^2(\theta)

    but I'm not sure how to get this in terms of t or if I even worked it out right. Also Im hoping I can replace my \vec{v}s in the formulas with u, I think I only need the magnitude for polar coords?

    any help would be appreciated greatly!
    Last edited by Snoopey; October 26th 2008 at 01:55 PM. Reason: added a bunch of latex code
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cylindrical polar coords
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 8th 2010, 03:55 AM
  2. Transforming polar to cartesian coords
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 2nd 2010, 02:16 PM
  3. Replies: 2
    Last Post: May 29th 2009, 05:57 AM
  4. Area between two curves in polar coords
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 22nd 2008, 04:32 AM
  5. Need help with double integral & polar coords
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 10th 2008, 11:20 PM

Search Tags


/mathhelpforum @mathhelpforum