calculus

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A police cruiser hunting for a suspect pulls over and stops at a point 10 ft from a straight wall.
The flasher on top of the cruiser revolves at a constant rate of 75 /second, and the light beam casts a spot of light as it strikes the wall.
How fast is the spot of light moving along the wall at a point 50 ft from the point on the wall closest to the cruiser?

<---10--->

  • calculus -

    If x is the distance from the closest point on the wall, then

    x = 10 tanθ
    dx/dt = 10 sec^2θ dθ/dt

    when x=50, tanθ = 5, so secθ = √26

    dx/dt = 10(26) (75)(2π) = 39000π ft/sec

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