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Math Help - Algebraic Manipulation involving Trigonometry

  1. #1
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    Algebraic Manipulation involving Trigonometry

    In a certain collision problem the kinematics are determined by the following three equations.

    u = v1cosθ + √(2)v2
    v1sinθ = √(2)v2

    1/2mu² = 1/2mv1² + 1/2(2m)v2²

    Use the first two equations to express v1 and v2 in terms of u, sinθ and cosθ. Then substitute into the third equation and obtain solutions for sinθ.

    --------------

    My working so far:

    u = v1cosθ + v1sinθ
    u = v1 (cosθ + sinθ )
    v1 = u/(cosθ+sinθ )
    v1² = u²/(cosθ + sinθ)²

    --------------

    v1 = u/( sinθ + cosθ )
    v1sinθ = √(2)v2
    usinθ/( sinθ + cosθ ) = √(2)v2
    u²sin²θ/( sinθ + cosθ )² = 2v2²
    1/2[u²sin²θ/( sinθ + cosθ )²] = v2²

    Are these two correct? and if so what should I do next?
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  2. #2
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    Joined
    Oct 2005
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    Quote Originally Posted by SunGod
    In a certain collision problem the kinematics are determined by the following three equations.

    u = v1cosθ + √(2)v2
    v1sinθ = √(2)v2

    1/2mu² = 1/2mv1² + 1/2(2m)v2²

    Use the first two equations to express v1 and v2 in terms of u, sinθ and cosθ. Then substitute into the third equation and obtain solutions for sinθ.

    --------------

    My working so far:

    u = v1cosθ + v1sinθ
    u = v1 (cosθ + sinθ )
    v1 = u/(cosθ+sinθ )
    v1² = u²/(cosθ + sinθ)²

    --------------

    v1 = u/( sinθ + cosθ )
    v1sinθ = √(2)v2
    usinθ/( sinθ + cosθ ) = √(2)v2
    u²sin²θ/( sinθ + cosθ )² = 2v2²
    1/2[u²sin²θ/( sinθ + cosθ )²] = v2²

    Are these two correct? and if so what should I do next?

    I'll attached my suggested solutions as followed:
    Attached Files Attached Files
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  3. #3
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    Joined
    Oct 2005
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    Thanks alot man, enjoy your positive rep.

    You made a mistake, sin²@+1 does not equal cos²@

    No matter I managed to fix it.
    Last edited by SunGod; October 27th 2005 at 12:01 PM.
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