An angler hooks a trout and reels in his line at 4 in. divided by s4 in./s. Assume the tip of the fishing rod is 13 ft13 ft above the water and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is 22 ft22 ft from the angler.

Question

Mathematics

Kamari Cross

11 May, 22:04

An angler hooks a trout and reels in his line at 4 in. divided by s4 in./s. Assume the tip of the fishing rod is 13 ft13 ft above the water and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is 22 ft22 ft from the angler.

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Brycen Wagner · Answer 1

The velocity of the reel is 4/4 = 1 in/s.

Draw a right triangle to illustrate the problem.

The hypotenuse represents the reel with a velocity of 1 in/s.

The vertical height of 13 ft represents the angler.

The horizontal length of 22 ft represents the distance of the trout from the angler.

Let x = angle between the hypotenuse and the horizontal.

By definition,

tan (x) = 13/22 = 0.5909

x = arctan (0.5909) = 30.58 deg.

The horizontal velocity is

v = (1 in/s) * cos (30.58 deg) = 0.86 in/s

Answer: 0.86 in/s