Solution:
Let O be the position of lighthouse.
Let A be the point on the shoreline closest to the lighthouse.
Let P be the point on the shoreline spotted by the lighthouse at a moment.
Let r be the distance between O and P.
Let θ be the angle between OA and OP.
∵Angular speed = 32π/min
∴Tangetial speed at point P = 32πr
∴Linear speed of point P moving along the shoreline
= 32πr/cosθ
= 32πr/(100/r)
= 8πr²/25
= 8π(100²+16²)/25
= 82048π/25
≈ 10310.46 (feet/min)