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Thread: Word Problem help?

  1. #1
    Junior Member
    Oct 2011

    Question Word Problem help?

    Two billiards balls collide and proceed to separate from one another at the same, constant speed. Assume the billiard table is frictionless. The angle between the balls is 1.25R. After 2 seconds, the distance between the ball is 1m. How fast are the balls moving?
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  2. #2
    Senior Member
    Nov 2013

    Re: Word Problem help?

    Before you even start make sure your calculator is set to radians.

    If the balls are traveling at the same speed then at any given point in time they will be the same distance from the point of collision.
    Hence the collision point and the position of the balls makes an isosceles triangle.

    It might be easier if I describe a picture and you draw it. I don't have the computer skills to draw it for you.
    Let the point of collision be C
    Let the position of the two balls after 2 seconds be X and Y
    CX=CY = distance the each ball has rolled = d
    If you draw a perpendicular line from C to XY you will have split the original triangle in half and you will have two right angled triangles.
    Let M be the point where this perpendicular cuts XY (M for midpoint)

    angle XCM = half of 1.25 radians = 0.625 Radians
    angle CMX is a right angle

    sin(0.625)=XM/CX = 0.5/d
    solve this to get d

    Now, speed=distance/time
    you now have distance and time is 2seconds so you can work out the speed.

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