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Homework Help: 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

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    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

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    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!!
     
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