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Math Help - Velocity Question

  1. #1
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    Velocity Question

    A ball is thrown straight down from the top of a 245 ft building with an initial velocity of -20 ft per second. What is its velocity after 4 seconds? What is its velocity after falling 100 ft?

    I have the first part = -148 ft/sec

    I cannot figure out what to do for the second part.
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  2. #2
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    Derivative of position-time gives velocity-time. Derivative of velocity-time gives acceleration.

    Well, we know the acceleration.
    a = 9.8

    So now if we take the integral of acceleration, we get velocity.
    v = 9.8x + c

    And we know that at 0 seconds, we're traveling -20ft/s
    -20 = 9.8(0) + c
    c = -20

    And so we get:
    v = 9.8x - 20

    The integral of this will then give us distance:
    d = \frac {9.8x^2}{2} - 20x + c

    And we know that we are 245 feet up at 0 seconds.

    245 = \frac {9.8(0)^2}{2} - 20(0) + c
    c = 245

    And thus our final equation:
    d = \frac {9.8x^2}{2} - 20x + 245

    You may recognize this last equation from physics class.

    d = (vi)t + 1/2at^2

    In the form of d - 245
    Last edited by derfleurer; April 21st 2009 at 05:46 PM.
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  3. #3
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    I understand what you are saying, but I don't understand how to apply the 100 ft...I need to find the velocity...
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  4. #4
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    Strange that they'd say a ball was thrown straight down and yet say it started at -20m/s rather than 20m/s. Still proper, but aimless, as you then must further assume acceleration to be negative (which I didn't).

    In which case,

    d = \frac {-9.8x^2}{2} - 20x + 245

    If you've fallen 100ft from 245ft

    245 - 100 = \frac {-9.8x^2}{2} - 20x + 245

    Solve for x and you get how many seconds you've been travelling. Plug that in for v = -9.8x - 20
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  5. #5
    MHF Contributor arbolis's Avatar
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    Alternatively in order to solve the second part you can use the conservation of mechanical energy, that is the formula E=\frac{mv^2}{2}+mgh=\text{a constant} .
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  6. #6
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    Without mass?
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  7. #7
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by derfleurer View Post
    Without mass?
    Are you talking to me? If so, I included mass (m) in the equation and it cancels out since E_{\text{initial}}=E_{\text{final}}.
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