Results 1 to 7 of 7

Math Help - chain rule. need an idea to start answering

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    151

    chain rule. need an idea to start answering

    hi there.. can someone just give me an idea to solve this problem?

    Two straight roads intersect at right angles. Car A, moving on one of the roads,
    approaches the intersection at 60km/h and Car B, moving on the other road,
    approaches the intersection at 80km/h. At what rate is the distance between the
    cars changing when A is 0.5km from the intersection and B is 0.7km from the
    intersection?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Think of ol' Pythagoras.

    The distance between the cars at the time they are .5 and .7 from the intersection, respectively, can be found from

    D=\sqrt{.5^{2}+.7^{2}}=.86 \;\ km

    Just differentiate implicitly w.r.t time, D^{2}=x^{2}+y^{2}

    D\frac{dD}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}

    \frac{dD}{dt}=\frac{x\frac{dx}{dt}+y\frac{dy}{dt}}  {D}

    Plug in your knowns on the right side (they are all given) and solve for dD/dt
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    151
    Quote Originally Posted by galactus View Post
    Think of ol' Pythagoras.

    The distance between the cars at the time they are .5 and .7 from the intersection, respectively, can be found from

    D=\sqrt{.5^{2}+.7^{2}}=.86 \;\ km

    Just differentiate implicitly w.r.t time, D^{2}=x^{2}+y^{2}

    D\frac{dD}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}

    \frac{dD}{dt}=\frac{x\frac{dx}{dt}+y\frac{dy}{dt}}  {D}

    Plug in your knowns on the right side (they are all given) and solve for dD/dt
    ok got it.. my answer is 100km..
    am i got it right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    That's what I got.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    151
    Quote Originally Posted by galactus View Post
    That's what I got.
    thanks galactus.. problem solved!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2009
    Posts
    151
    regarding the solution above, should i get the answer is -100km/h
    should take in account the vector of this question?
    Attached Thumbnails Attached Thumbnails chain rule. need an idea to start answering-cars.jpg  
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Nov 2009
    Posts
    263
    because the distance between the cars getting closer, i think the minus sign is needed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. No idea where to start
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 3rd 2010, 12:06 PM
  2. Complex number.. need an idea to start..
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 29th 2009, 03:59 PM
  3. No idea where to start
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 24th 2009, 11:32 PM
  4. Replies: 4
    Last Post: April 13th 2009, 06:26 PM
  5. [SOLVED] No idea where to start!
    Posted in the Algebra Forum
    Replies: 11
    Last Post: July 25th 2008, 10:44 AM

Search Tags


/mathhelpforum @mathhelpforum