**Reeling in the Catch: Understanding Linear Speed of a Fishing Line**As Tony the fisherman reels in a "big one," he turns the spool on his fishing reel at a constant rate of 3.6 revolutions every second.**Illustration:**The image depicts a fisherman, Tony, reeling in a fish. The fishing rod is bent, indicating tension, and the fishing line is visibly taut as the fish is being pulled from the water. An arrow marked 'v' shows the direction of the reel’s rotation.**Problems and Solutions:**(a) **Calculating Linear Speed When Outer Radius is 3.4 cm:**- **Question:** What is the linear speed of the fishing line as it is reeled in?- **Given Data:** Outer radius = 3.4 cm, Rotation rate = 3.6 revolutions per second\[ \text{Linear speed} = 2 \pi \times \text{radius} \times \text{rotation rate} \](Fill in the formula with the given numbers to solve.)(b) **Re-evaluation with Outer Radius of 6.8 cm:**- **Question:** What is the new linear speed with the updated radius?- **Given Data:** Outer radius = 6.8 cm(Use the same formula with the new radius to find the updated speed.)(c) **Time Analysis for Equal Distance Halves:**- **Question:** Assuming Tony maintains this constant rotation rate, which half of the trip will take more time? **Options:**- The first half (from the catch point to the halfway point)- The second half (from the halfway point to the boat)- N/A - they will take the same time(Consider the linear speed calculations to answer this.)This exercise allows you to explore the principles of rotational motion and how changes in radius affect linear speed.

Given data: Angular velocity, ω=3.6 rev/s Outer radius, r=3.4 cm

As Tony the fisherman reels in a "big one" he turns the spool on his fishing reel at a constant rate of 3.6 revolutions every second. (a) When the outer radius of the fishing line on the spool is 3.4 cm, what is the linear speed of the fishing line as it is reeled in? cm/s (b) Later on, when enough string has accumulated on the spool so that its outer radius is now 6.8 cm, re-evaluate part a. cm/s (c) Suppose we split the total distance the fish must travel to the boat into two equal halves. Assuming Tony maintains this constant rotation rate, which half of the trip will take more time? ---Select--- the first half (from the catch point to the halfway point) the second half (from the halfway point to the boat) N/A - they will take the same time

As Tony the fisherman reels in a "big one" he turns the spool on his fishing reel at a constant rate of 3.6 revolutions every second. (a) When the outer radius of the fishing line on the spool is 3.4 cm, what is the linear speed of the fishing line as it is reeled in? cm/s (b) Later on, when enough string has accumulated on the spool so that its outer radius is now 6.8 cm, re-evaluate part a. cm/s (c) Suppose we split the total distance the fish must travel to the boat into two equal halves. Assuming Tony maintains this constant rotation rate, which half of the trip will take more time? ---Select--- the first half (from the catch point to the halfway point) the second half (from the halfway point to the boat) N/A - they will take the same time

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

**Reeling in the Catch: Understanding Linear Speed of a Fishing Line**

As Tony the fisherman reels in a "big one," he turns the spool on his fishing reel at a constant rate of 3.6 revolutions every second.

**Illustration:**
The image depicts a fisherman, Tony, reeling in a fish. The fishing rod is bent, indicating tension, and the fishing line is visibly taut as the fish is being pulled from the water. An arrow marked 'v' shows the direction of the reel’s rotation.

**Problems and Solutions:**

(a) **Calculating Linear Speed When Outer Radius is 3.4 cm:**

- **Question:** What is the linear speed of the fishing line as it is reeled in?
- **Given Data:** Outer radius = 3.4 cm, Rotation rate = 3.6 revolutions per second

\[ \text{Linear speed} = 2 \pi \times \text{radius} \times \text{rotation rate} \]

(Fill in the formula with the given numbers to solve.)

(b) **Re-evaluation with Outer Radius of 6.8 cm:**

- **Question:** What is the new linear speed with the updated radius?
- **Given Data:** Outer radius = 6.8 cm

(Use the same formula with the new radius to find the updated speed.)

(c) **Time Analysis for Equal Distance Halves:**

- **Question:** Assuming Tony maintains this constant rotation rate, which half of the trip will take more time?

**Options:**
- The first half (from the catch point to the halfway point)
- The second half (from the halfway point to the boat)
- N/A - they will take the same time

(Consider the linear speed calculations to answer this.)

This exercise allows you to explore the principles of rotational motion and how changes in radius affect linear speed.

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