1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Related Rates

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    (Q) A lamp is placed at the point (5,0) and it casts the shadow of an ant onto the y axis. When the ant is at point (1,2), how fast is the ant's shadow moving when the ant's x-coordinate is increasing at the rate of 1/2 units/sec and its y-coordinate is decreasing at 1/5units/sec?

    I got -9/16. Is it correct? I just need to confirm whether I'm right or wrong.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 27, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    That's not at all what I get. Too bad you didn't show your working- I might have been able to point out an error.
     
  4. Nov 27, 2007 #3
    Here we go!!

    Let the coordinates of the ant be x,y. Let the length of the shadow be s.

    Our goal is to find ds/dt. By similar triangles, s/y = 5/(5-x).

    So, 5s - sx = 5y
    Differentiating,

    5(ds/dt) - (s(dx/dt) + x(ds/dt)) = 5(dy/dt)

    When (x,y) = (1,2), s = 5/2.

    5(ds/dt) - (5/2)(1/2) - (1)(ds/st) = 5(-1/5).

    4(ds/dt) = -9/4.

    ds/st = -9/16
     
  5. Nov 27, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You "lost a sign"
    4(ds/dt)= +5/4- 1= 1/4, not -9/4.

     
  6. Nov 27, 2007 #5
    Dammit!!

    All because of this gross gross gross error, I got the answer wrong in the exam. How many marks do you think I'll lose (out of 5?).??

    Thanks a ton!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Related Rates
  1. Related rates formula (Replies: 3)

  2. Related Rates (Replies: 2)

Loading...