Asked by TayB
Related Rates: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
Answers
Answered by
Steve
the light turns through angle θ where dθ/dt = 4π.
If the light hits x km away from P, then
x = 4tanθ
So,
knowing that tanθ = 1/4, plug in the numbers and find dx/dt:
dx/dt = 4 sec^2(θ) dθ/dt
If the light hits x km away from P, then
x = 4tanθ
So,
knowing that tanθ = 1/4, plug in the numbers and find dx/dt:
dx/dt = 4 sec^2(θ) dθ/dt
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