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.)

Answer 1

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