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Math Help - Relative Velocity

  1. #1
    Member srirahulan's Avatar
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    Arrow Relative Velocity

    3 particles A,B,C are projected from a point above the ground level.A launches horizontally with a velocity of U and B, was launches 90-\thetafrom vertical with the velocity of W and C was launches vertically with the velocity of V.Using the relative velocity, If \frac{cos\theta}{U}+\frac{sin\theta}{V}=\frac{1}{W  },Show that The particles A,B,C are in a straight line??

    In this case Give me hint to use Relative velocity>>><<<<
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  2. #2
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    Re: Relative Velocity

    Quote Originally Posted by srirahulan View Post
    3 particles A,B,C are projected from a point above the ground level.A launches horizontally with a velocity of U and B, was launches 90-\thetafrom vertical with the velocity of W and C was launches vertically with the velocity of V.Using the relative velocity, If \frac{cos\theta}{U}+\frac{sin\theta}{V}=\frac{1}{W  },Show that The particles A,B,C are in a straight line??

    In this case Give me hint to use Relative velocity>>><<<<
    looking at the velocity vectors

    \begin{align*}&v_A=\{U,0\} \\ &v_B=\{W \cos(\theta),W \sin(\theta)\} \\ &v_C=\{0,V\}\end{align}

    so for a given t=T

    \begin{align*}&p_A=\{UT,0\} \\ &p_B=\{W \cos(\theta)T,W \sin(\theta)T\} \\ &p_C=\{0,VT\}\end{align}

    now find the equation of the line determined by p_A$ and $p_C and show that your constraint equation leads to B lying on this line.
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  3. #3
    Member srirahulan's Avatar
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    Re: Relative Velocity

    please Give me more Information>>>>
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  4. #4
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    Re: Relative Velocity

    you give me information

    can you find the equation of the line that connects particle A and particle C ? If not, why not?
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  5. #5
    Member srirahulan's Avatar
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    Re: Relative Velocity

    yes i find out the equation,then what can i do>>>>
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  6. #6
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    Re: Relative Velocity

    show that p_B is on this line given it's coordinates at time T that I showed a couple posts ago. You'll see the condition that B is on this line is identical to the equation you are given relating the velocities of the 3 particles.
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