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Math Help - Integration help please

  1. #1
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    Integration help please

    Can anyone help with this? I cant integrate at all


    (a)You decide to make a accurate estimation of the height of a bridge by considering air resistance. By doing a little research you discover that, for a stone, the air resistance (R) is proportional to velocity such that R = 0.009V for that type of stone. If the mass of the stone is 0.4 kg and g = 9.8 ms-2, then apply Newton’s second law of motion to prove that: dv/dt = 9.8-0.225v

    (b) This is known as a variable-separable differential equation, which can be written as:
    \int 1/ 9.8-0.0225v dv = \int dt

    By solving these integrals find
    (i) t as a function of v, from which find
    (ii) v as a function of t, i.e. show that v=436-435e^-0.0225t

    (c) Using v=dx/dt find x as a function of t.

    (d) If t = 5 seconds, then what is the height of the bridge? Calculate the percentage error using S = Ut + ½ at2 where a = g = 9.8
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  2. #2
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    Re: Integration help please

    I presume you mean \int \frac{1}{9.8- 0.0225v}dv. Let u= 9.8- 0.0225v.

    (What you wrote was \int (\frac{1}{9.8}- 0.0225v)dv.)
    Last edited by HallsofIvy; March 16th 2013 at 09:33 AM.
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  3. #3
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    Re: Integration help please

    Yea thats what i meant. Thanks
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  4. #4
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    Re: Integration help please

    Solved it. Thanks anyway.
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