Asearchlight is located at a perpendicular distance of 315 yards from a fixed point f on a straight shoreline. this light revolves at 1 revolution per minute. how fast does its beam sweep along the shoreline at a point p, 425 yards downshore from f?

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