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Math Help - Basic rearranging

  1. #1
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    Basic rearranging

    I am currently solving questions preparing for my mechanics exam and I am struggling with the final part of the question I have the following equation

    y-yo=Vo*sin(beta)*x^2/Vo*cos(beta)-1/2*g*x^2/Vo^2cos^2(beta)

    I need to solve this for Vo any help would be much appreciated
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  2. #2
    Super Member Bacterius's Avatar
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    I'm sorry but this is ambigious. I'll just put what I think the equation is into proper LaTeX form, and please tell us if this is the right one.

    y - y_0=V_0 \times \sin{(\beta)} \times \frac{x^2}{V_0} \times \cos{(\beta)} - \frac{1}{2} \times g \times \frac{x^2}{V_0^2} \times \cos^2{(\beta)}

    Is this the one ?
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  3. #3
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    Sorry your right that is the correct equation could you please point me in the right direction on how to solve for Vo
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  4. #4
    MHF Contributor

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    Assuming that is correct the V_0 and \frac{1}{V_0} in the first term will cancel leaving
    y- y_0= sin(\beta)cos(\beta)-\frac{1}{2}g\frac{x^2}{V_0^2}cos^2(\beta)

    Subtract sin(\beta)cos(\beta) from both sides:
    y- y_0- sin(\beta)cos(\beta)= -\frac{1}{2}g\frac{x^2}{V_0^2}cos^2(\beta)

    Multiply both sides by V_0^2:
    V_0^2(y- y_0- sin(\beta)cos(/beta))= -\frac{1}{2}gx^2cos^2(\beta)

    Divide both sides by y- y_0- sin(\beta)cos(/beta):
    V_0^2= -\frac{gx^2cos^2(\beta)}{2(y- y_0- sin(\beta)cos(\beta)}

    And, finally, take the square root of both sides:
    V_0= \sqrt{-\frac{gx^2cos^2(\beta)}{2(y- y_0- sin(\beta)cos(\beta))}}

    V_0= \sqrt{\frac{gx^2 cos^2(\beta)}{2(sin(\beta)cos(\beta)- y+ y_0)}}
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  5. #5
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    thankyou this has been very helpful
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