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.

Question

Mathematics

Reese Solis

28 July, 19:13

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.

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Hallie Boyle · 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