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Math Help - Application of derivatives

  1. #1
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    Application of derivatives

    A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)
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  2. #2
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    hello

    why nobody help?
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  3. #3
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    Quote Originally Posted by Joyce View Post
    A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)
    hello,

    I've attached a drawing of the situation.

    You are dealing with 2 similar triangles. You can set up the proportion:

    \frac s{30} = \frac{30-s}y. Solve for y because that's the length which the shadow of the ball is away from the pole:

    y=\frac{900}s - 30 . You are told that s = 16t^2 . Substitute the variable s and you'll get the equation:

    y(t) = \frac{900}{16t^2}-30

    You know that speed is the first derivative wrt t of the length:

    y'(t) = -\frac{900}{8t^3}

    The speed at t = \frac12 is:

    \rm{speed} = y'\left(\frac12 \right) = -\frac{900}{8 \cdot \frac18} = -900
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  4. #4
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    Quote Originally Posted by Joyce View Post
    why nobody help?
    I'm an infirm old man and need some time to type the solution and to make a nice drawing. I'm now really breathless and exhausted
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