Distance to the lighthouse from point F= 315 yards
Distance to the point P = 425 yards
Pythagorean theorem for the distance from lighthouse to point (P)
= âš(315)^2 + (425)^2 = 529 yards
The lighthouse beam makes 1 full revolutions in a minute.
So, we can express the angular speed as: w = 1 rev/min
The beam sweeps around the circle in a circular path. So we want to find the speed along the circumference of a circle of an object moving at 1 rev/min.
From circumference of a circle C = 2 * pie * r. Here r = 529
Since the circumference is the same as the distance traveled around the circle.
I. e 1 revolution 1 rev = 2 * pi * r
So we have 1 rev/min = 2 * pie * r/min = 2 * pie * 529/min = 1058 *pie/min = 3324.126/min
