A light house is located on a small island 3 km away from the nearest point P on a straight shoreline and the light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km away from P?
+118724 A light house is located on a small island 3 km away from the nearest point P on a straight shoreline and the light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km away from P?
Distance of light house to new point is sqrt(9+1)=sqrt10
Circumference of circle with radius of sqrt(10) = 2pi* sqrt(10)
The light is travelling at 4 rvs per minute which is equal to 1 rev per (1/4) minute
so
speed = distance / time
\(speed = 2\pi\sqrt{10}\div \frac{1}{4}\;\;km/min\\ speed = 2\pi\sqrt{10}\times 4\;\;km/min\\ speed = 4\pi\sqrt{10}\;\;km/min\\ speed = 4\pi\sqrt{10}\;\;km/min\\ speed \approx 39.73835\;\;km/min\\ speed \approx 39.73835*60\;\;km/hour\\ speed \approx 2384\;\;km/hour\\ \)
