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Math Help - wheel trig problem

  1. #1
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    wheel trig problem

    A pebble is wedged in the bottom of a tire. The horizontal distance of the pebble from the left-most edge of the tire varies sinusoidally with the distance you have traveled. Diameter is 5pi inches

    L=distance of the pebble from the left-most edge of the tire after you have traveled x inches. Write en equation relating L and X….work in degrees and radians? Degrees first I guess than convert…I dno.


    Then…..determine the first positive x value that makes L = 1
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  2. #2
    Junior Member qspeechc's Avatar
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    Draw a picture, as you should do with all problems. Now, when the tire travels x inches forward, it means the circumference has moved along x inches. This means, that if the stone started at the bottom, it has now moved backwards by an angle θ relative to a vertical through the axis. The angle subtends a circumference of length x. The radius of the wheel is 2.5π inches. θ = arc length/radius = x/2.5π
    Now, the pebble starts 5π inches to the right of the left most point. After the wheel goes forward x inches, the pebble moves back θ radians, so the distance backwards it moves is 5πsinθ inches (look at your diagram, draw a right angled triangle with hypotenuse equal to the radius of the wheel, when the stone has moved back by θ radians). So now the distance the stone is from the left most point, after it has moved forward x inches, is:
    5π - 5πsinθ = 5π(1 - sinθ)
    This is the distance L and we know θ = x/2.5π, so:
    L = 5π[1 - sin(x/2.5π)]

    I am sorry, I just can't seem to get this all the same font and size
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  3. #3
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    that isnt right because you are not measuring the diagonal line from the leftmost point to the point where the pebble is now....that is L
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  4. #4
    Junior Member qspeechc's Avatar
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    Well that is simple; just construct another right-angled triangle and use some geometry.
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