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Math Help - The garden roller problem (trigonometry)

  1. #1
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    The garden roller problem (trigonometry)

    The diagram below shows a simplified side view of a garden roller. The radius of the cylinder is 30 cm. The length of the handle is 130 cm. The roller is leaning against a wall with the handle at an angle of 25 degrees to the vertical the ground is horizontal.

    A gardener takes the roller on to a lawn. Just as he begins to roll he notices a small scratch at the highest point of the cylinder.

    (iv) Show that, when the cylinder has been pushed a distance x cm on the lawn, the height of the scratch above the ground is:

    30{1+cos(6x/pi)}cm

    Anyone know how to get there?
    Attached Thumbnails Attached Thumbnails The garden roller problem (trigonometry)-gardenroller.gif  
    Last edited by Trigo; August 16th 2005 at 02:21 PM.
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  2. #2
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    What scratch?
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  3. #3
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    I have now added the missing information. My apologies.
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  4. #4
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    If the roller has been pushed x cm along the ground, it has rotated by the x/(circumference) of a revolution: that is, by x/30 radians or 360x/(2.pi.30) degrees. So the height of the scratch above the level of the centre is now 30cos(60x/pi): draw a picture showing the roller rotated by 60x/pi. The centre is itself 30 cm above the ground.
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  5. #5
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    Thank you
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