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Rate of change of the area of the rebgion

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing?

    2. Relevant equations
    a=1/2bh


    3. The attempt at a solution
    x^2 + 4^2= 5^2
    x=3
    da/dt= 1/2b(db/dt)(dh/dt)

    I think i started it up wrong and I don't know where to go next..
     
  2. jcsd
  3. Nov 11, 2012 #2

    SammyS

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    What is the shape of the region below the board and above the ground at the moment under consideration?
     
  4. Nov 11, 2012 #3
    just a normal triangle drawn on a line like a typical triangle leaning against a wall problem.
     
  5. Nov 11, 2012 #4

    SammyS

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    Neither end of the board is touching the ground, so it's not a triangle.
     
  6. Nov 11, 2012 #5
    Have another look at that derivative. It looks like the product rule hasn't been applied properly. Also one of those b/h is x. You'll have to stay consistent with your variable names.
     
  7. Nov 11, 2012 #6
    Re: rate of change of the area of the region

    http://img231.imageshack.us/img231/5130/scan0060kd.jpg [Broken]

    that is how it looks
     
    Last edited by a moderator: May 6, 2017
  8. Nov 11, 2012 #7

    SammyS

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    Re: rate of change of the area of the region

    You're right. I misread the problem.

    When you said x=3, that should be h=3 .

    In general, how are b and h related, considering that they're legs of a right triangle?
     
    Last edited by a moderator: May 6, 2017
  9. Nov 12, 2012 #8
    i said b= 4ft and h=3 ft
     
  10. Nov 12, 2012 #9

    SammyS

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    That's what b & h are at the instant that h = 4 ft, but how are they related in general?

    (Use the Pythagorean theorem.)
     
  11. Nov 12, 2012 #10

    Ray Vickson

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    The crucial point that you seem to be missing is that you need to figure out what is happening as the board slides down the wall, so h moves from more than 3 ft to less than 3 ft (and, at the same time, b moves from less than 4 ft to more than 4 ft). When that is happening, the area of the triangle is changing, and that is what you are supposed to be reckoning. So, you need to let b and h be variables, not fixed numbers.

    RGV
     
  12. Nov 12, 2012 #11

    SammyS

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    Of course, that's a typo !!!

    It should have said:
    That's what b & h are at the instant that b = 4 ft, but how are they related in general?
     
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