Answered: The eye of a hurricane passes over…

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)...

See similar textbooks

Related questions

Concept explainers

Question

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 38.5 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 23.5 km/h. How far from Grand Bahama is the hurricane 4.45 h after it passes over the island?

Step 1

Assume that the Grand Bahama Island lies at the origin of the coordinate system shown in the diagram at below. Vector represents the hurricane's displacement at 38.5 km/h and vector represents its displacement after it shifts course three hours later and proceeds at a speed of 23.5 km/h. Vector represents the hurricane's displacement after a total time of 4.45h.

A coordinate plane has a horizontal, leftward axis labeled "west" and a vertical, upward axis labeled "north". Three vectors are plotted.

Vector A starts at the origin and points up and to the left at an angle of 60.0° above the horizontal axis.
Vector B, which is much shorter than vector A, starts at the tip of vector A and points vertically upward.
Vector R starts at the origin and moves up and to the left, ending at the tip of vector B.

Vector in the diagram has components to the west and to the north in this coordinate system while vector has only a north component. During the first three hours after passing the island, the displacement of the hurricane is represented by vector , and the storm travels a distance that is the magnitude of . This distance is

### Tutorial Exercise

**Problem Statement:**
The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 38.5 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 23.5 km/h. How far from Grand Bahama is the hurricane 4.45 hours after it passes over the island?

### Step 1

**Assumptions and Diagram:**
Assume that the Grand Bahama Island lies at the origin of the coordinate system shown in the diagram below.

- Vector \( \vec{A} \) represents the hurricane's displacement at 38.5 km/h.
- Vector \( \vec{B} \) represents its displacement after it shifts course three hours later and proceeds at a speed of 23.5 km/h.
- Vector \( \vec{R} \) represents the hurricane's displacement after a total time of 4.45 hours.

![Hurricane Path Diagram](image_url)

In the diagram:
- Vector \( \vec{A} \) has components to the west and to the north.
- Vector \( \vec{B} \) has only a north component.

During the first three hours after passing the island, the displacement of the hurricane is represented by vector \( \vec{A} \), and the storm travels a distance that is the magnitude of \( \vec{A} \). This distance is:

\[ A = v_1 \Delta t_1 = \]

\[ \] km/h \[ \] km

#### Error Messages:
- Your response differs from the correct answer by more than 100%. km/h \[ \] km
- Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. \( h \) = \[ \] km
- Your response differs from the correct answer by more than 10%. Double check your calculations. km and the associated vector \( \vec{A} \) is in a direction 60.0° north of west.

**Note:**
The explanations and calculations here are structured to aid in problem-solving and conceptual understanding of vectors and their applications in real-world scenarios such as tracking hurricane paths.

### Need Help?
Read It (Hyperlink to further material or guidance)

(Note: Replace the placeholder image URL with the actual URL if the image is

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions