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9 November, 14:57

A rotating light is located 13 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.

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  1. 9 November, 16:09
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    29.2 ft/s

    Explanation:

    The distance of the light's projection on the wall

    y = 13 tan θ

    where θ is the light's angle from perpendicular to the wall.

    The light completes one rotation every 3 seconds, that is, 2π in 3 seconds,

    Angular speed = w = (2π/3)

    w = (θ/t)

    θ = wt = (2πt/3)

    (dθ/dt) = (2π/3)

    y = 13 tan θ

    (dy/dt) = 13 sec² θ (dθ/dt)

    (dy/dt) = 13 sec² θ (2π/3)

    (dy/dt) = (26π/3) sec² θ

    when θ = 15°

    (dy/dt) = (26π/3) sec² (15°)

    (dy/dt) = 29.2 ft/s
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