Final answer:
By using the Pythagorean Theorem and considering the reeling speed as the rate of change of the hypotenuse, the horizontal speed of the fish when it is 16 ft from the angler is found to be about 3 in./s.
Step-by-step explanation:
To determine the horizontal speed of the fish when it is 16 ft from the angler, we can use the Pythagorean Theorem. This involves setting up a right triangle with the tip of the fishing rod above the water as one leg (11 ft), the distance of the fish from the angler as the other leg (16 ft), and the hypotenuse as the line from the rod tip to the fish. Since the reeling speed is the speed of the hypotenuse shortening (3 in./s), we need to find the horizontal component of this speed.
Let's convert feet to inches to match the reeling speed, which is given in inches per second: 11 ft = 132 inches and 16 ft = 192 inches.
We can write the following relationships using the derivatives (as the sides of the triangle change with time) related to the Pythagorean Theorem: (d(hypotenuse)/dt)² = (d(horizontal distance)/dt)² + (d(vertical distance)/dt)².
Substituting the known values and solving for the horizontal speed, we get:
(3 in./s)² = (d(horizontal distance)/dt)² + 0 (since the vertical distance is constant),
which simplifies to (d(horizontal distance)/dt)² = (3 in./s)².
Thus, d(horizontal distance)/dt = 3 in./s, which means the horizontal speed of the fish when it is 16 ft from the angler is about 3 in./s.
The correct answer is b) When the fish is 16 ft from the angler, its horizontal speed is about 3 in./s.