Question

The tip of a fisherman's fishing rod is 15 feet above the water, and he has 25 feet of line out when he feels the tug of the fish. He reels in his line at a rate of 0.5 feet per second. We are assuming that the fish is near the water surface throughout the process.

a. How much line is out after 5 seconds? Include units.
b. Find the average velocity on the interval [0, 5] at which the fish is being pulled toward the fisherman during the first 5 seconds. Include units.

Answer 1

After 5 seconds, the fisherman will have 22.5 feet of line out. The average velocity of the fish being pulled toward the fisherman during the first 5 seconds is 2.5 feet per second.

Step-by-step explanation:

To find how much line is out after 5 seconds, we need to determine how much line the fisherman has reeled in. Given that the fisherman reels in the line at a rate of 0.5 feet per second, after 5 seconds he will have reeled in 5 * 0.5 = 2.5 feet of line. Since he initially had 25 feet of line out, he will still have 25 - 2.5 = 22.5 feet of line out after 5 seconds.

To find the average velocity at which the fish is being pulled toward the fisherman during the first 5 seconds, we first need to determine the change in position of the fish during this time. The fisherman initially had 15 feet of line above the water, and after 5 seconds he has reeled in 2.5 feet. Therefore, the change in position of the fish is 15 - 2.5 = 12.5 feet. The average velocity is found by dividing the change in position by the time taken, which is 12.5 / 5 = 2.5 feet per second.