http://www.saylor.org/site/wp-content/uploads/2011/06/MA101-3.5.1.pdf :: 6.2.5 =

A rotating beacon is located 2 miles out in the water. Let A be the point on the shore that
is closest to the beacon. As the beacon rotates at 10 rev/min, the beam of light sweeps down
the shore once each time it revolves. Assume that the shore is straight. How fast is the point
where the beam hits the shore moving at an instant when the beam is lighting up a point 2
miles along the shore from the point A?

Question

http://www.saylor.org/site/wp-content/uploads/2011/06/MA101-3.5.1.pdf :: 6.2.5 =

A rotating beacon is located 2 miles out in the water. Let A be the point on the shore that
is closest to the beacon. As the beacon rotates at 10 rev/min, the beam of light sweeps down
the shore once each time it revolves. Assume that the shore is straight. How fast is the point
where the beam hits the shore moving at an instant when the beam is lighting up a point 2
miles along the shore from the point A?

anonymous · Answer

$$x^2+y^2=r^2 => 2xx'+2yy'=2rr' => 0+4y'=2\sqrt8r'$$
$$y=rsinθ =>yy'=r'\sinθ+rcosθθ' => 2y'=r'2/\sqrt8+\sqrt82/\sqrt8ω$$