Question

A fisherman hooks a trout and reels in his line at 4 ​in/s. Assume the tip of the fishing rod is 10 ft above the water and the fish is pulled horizontally directly towards the fisherman​ (see figure). Find the horizontal speed of the fish when it is 30 ft from the fisherman.

Answer 1

Let x be the distance of the fish to the fisherman and h be the height of the tip of fishing rod then we want to fiind dx/dt when x = 20. By property of similar triangle we have 12/x = h/20 --> h = 240/x
Differentiating w.r.t. we obtain dh/dt = (-240/x^2)*dx/dt --> dx/dt = [-(x^2)/240]*dh/dt
At x = 20, dh/dt = 4 --> dx/dt = (-400/240)*4 = 20/3