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Math Help - vector problem

  1. #1
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    vector problem

    Kindly guide me in the following vector problem:

    Magnitude of a velocity vector is 10 m/s. If theta = 30 degrees, find its (i) x component (ii) y component. Theta is measured from +ve side of the y-axis. Hope I have made myself clear.

    Thanks for the help.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: vector problem

    Draw a sketch. Draw your x and y axes, draw the vector originating from the origin and 30 less than vertical. Label the angle. From the terminus of the vector draw a horizontal line segment to the y-axis. This segment is your x-component and the length along the y-axis from the origin to the point where the horizontal segment meets the y-axis is your y-component.

    The magnitude of the vector is the hypotenuse, how do you find length of the legs, i.e., the x and y components?
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  3. #3
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    Re: vector problem

    cos 30 = opp/10 ; sin 30 = adj/10; cos 30 = sq.root of 3 /2 and sin 30 = 1/2 ;

    Is the method correct?

    Thank u
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: vector problem

    You have the definitions of sine and cosine reversed, but you are on the right track. What is probably throwing is that usually the angles are measured from the positive x-axis in a counter-clockwise motion. The angle in this problem is measured from the positive y-axis, where I am assuming in a clockwise motion. If that's not the case, then we just reverse the sign of the x-component.

    To find the x-component v_x:

    \sin\(30^{\circ}\)=\frac{v_x}{10} solve for v_x

    To find the y-component v_y:

    \cos\(30^{\circ}\)=\frac{v_y}{10} solve for v_y
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