Results 1 to 7 of 7

Math Help - Rod and Wheel Calculus question

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    5

    Rod and Wheel Calculus question

    Ok so I am struggling with a question that I have been trying to figure out for a couple of days now. The professor told us the first part but i can't figure out the rest. Here is the question from the attached files:
    Rod and Wheel Calculus question-pow-5-mth-151_page_1.jpg
    Rod and Wheel Calculus question-pow-5-mth-151_page_2.jpg

    According to our professor, question 1 becomes:

    X(t) = 2[cos(7πt) + sqrt(9-sin2(7πt))]

    Jest before someone asks, it is not graded HWK. It is an application problem which encompasses many of the things we have learnt in the last week. We get them every week and must try to get them (not necessary though).
    Last edited by mr fantastic; October 31st 2010 at 01:08 PM. Reason: Title.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    What exactly is your problem? I got the same result for x(t). The angular speed is (7/2) * (2π radians) / (1 min) = 7π radians/min. Therefore, the angle the radius to point A makes at time t is 7πt radians. Next, x(t) is the sum of the projection of A, i.e., 2cos(7πt), and the projection of the rod, which can be found using Pythagoras theorem (the y-coordinate of A is 2sin(7πt)).

    The derivative can be found using the chain rule. It's a big expression, but sin(7πt) can be factored out. One can show that the second factor cannot equal zero. Therefore, x'(t) = 0 iff sin(7πt) = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    5
    ok... how do I go about proving that x'(t) = 0? It asks to use Calculus and I need points.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    I am not sure I understand your question. You can't prove that x'(t) = 0 for every t. So for what t do you want to prove it and why?

    You are asked to find t such that the speed of B at time t is zero. By calculating the speed of B as the derivative x'(t), you have already used calculus. Next, you need to solve the equation x'(t) = 0. As I said, this equation is equivalent to sin(7πt) * f(t) = 0 for some function f(t). I believe it it possible to show that f(t) is never zero. Therefore, x'(t) = 0 iff sin(7πt) = 0. You should be able to solve the latter equation.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2010
    Posts
    5
    ok I understand... I was making it more complicated than it had to be... so the only way for sin(7πt) = 0 is if t = 0 right?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    No, also when 7πt = π, 2π, 3π and in general kπ for some integer k.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2010
    Posts
    5
    right! Sorry about that and thanks for all the help! Greatly appreciated
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 18th 2010, 09:03 AM
  2. Ferrish Wheel Question
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: October 4th 2010, 04:49 PM
  3. Rotating Water Wheel question.
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 24th 2010, 02:46 PM
  4. Wheel Question
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 12th 2009, 08:18 PM
  5. Ferris wheel problem calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 3rd 2008, 01:47 PM

Search Tags


/mathhelpforum @mathhelpforum