A lighthouse containing a revolving beacon is located 3 km from P,the nearest point on a straight shoreline.?

Question

A lighthouse containing a revolving beacon is located 3 km from P,the nearest point on a straight shoreline.

The beacon revolves with a constant rotation rate of 4 revolutions per minute and throws a sport of light onto the shoreline. How far is the spot of light moving when it is at a point on the shoreline 2 km from P?

The answer is 104pi/3 km/min. How do you get this?

Answer 1

x = (3 km)tanθ

v = dx/dt = (3 m)sec^2θdθ/dt

v = (3 km)(4 rev/min)/cos^2θ

v = (3 km)(8π rad/min)/[3/√(9 + x^2)]^2

v = (3 km)(8π rad/min)/[3/√(9 + 4)]^2

v = (3 km) (8π rad/min)(13)/9

v = 104π/3 km/min