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Math Help - Integrals! :)

  1. #1
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    Integrals! :)

    I have a homework problem that I need help on:

    A stone is dropped from the edge of a roof, and hits the ground with a velocity of -175 ft/s. How high (in feet) is the roof?

    I know that the acceleration would be -32ft/s due to gravity, so v(t)=-32t+c.
    However, since I don't know how long it takes for the stone to hit the ground, I don't know what to use for time, or my constant c. Can you help me to work through this problem? Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tennisgirl View Post
    I have a homework problem that I need help on:

    A stone is dropped from the edge of a roof, and hits the ground with a velocity of -175 ft/s. How high (in feet) is the roof?

    I know that the acceleration would be -32ft/s due to gravity, so v(t)=-32t+c.
    However, since I don't know how long it takes for the stone to hit the ground, I don't know what to use for time, or my constant c. Can you help me to work through this problem? Thanks!
    You've got the right start. Let's back up a bit on that velocity equation.

    \frac{dv}{dt} = -32

    dv = -32~dt

    \int_{v_0}^v dv = -32 \int_0^t dt

    v - v_0 = -32t

    v = -32t + v_0

    So we see that the constant is the velocity of the object at t = 0. (We could have gone straight to this result, but I feel this explanation is more "transparent.")

    Once you have v0 you can integrate again:
    \frac{dx}{dt} = -32t + v_0

    and get
    x = x_0 + v_0t - 16t^2
    and get your height.

    By the way, there is a much faster way to do this, but it's a more "Physicsy" way of doing things:
    v^2 = v_0^2 + 2a(x - x_0)

    -Dan
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by tennisgirl View Post
    I have a homework problem that I need help on:

    A stone is dropped from the edge of a roof, and hits the ground with a velocity of -175 ft/s. How high (in feet) is the roof?

    I know that the acceleration would be -32ft/s due to gravity, so v(t)=-32t+c.
    However, since I don't know how long it takes for the stone to hit the ground, I don't know what to use for time, or my constant c. Can you help me to work through this problem? Thanks!
    Double integrate
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