calculus

a laser printer is placed on a platform that rotates at a rate of 20rev/min. the beam hits a wall 8m away producing a dot of light that moves horizontally along the wall. let tetabe the angle between the bean and producing the line through the search light perpendicular to the wall. how fast is that dot moving when teta = pie/6 ?

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asked by dinesh
  1. As usual, draw a diagram. If x is the distance of the beam from the perpendicular line to the wall, then

    x/8 = tanθ
    x = 8tanθ

    So,

    dx/dt = 8sec^2θ dθ/dt
    When θ = π/6 (and that's pi, not pie!!)
    dx/dt = 8(4/3)(20*2π) = 1280π/3 m/s

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    posted by Steve

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