### Problem Statement:Car A rounds a curve of 172-m radius at a constant speed of 37 km/h. At the instant represented, car B is moving at 97 km/h but is slowing down at the rate of 2.5 m/s². Determine the velocity and acceleration of car A as observed from car B.### Diagram:The image shows a diagram of a crossroad with two cars, Car A and Car B. Car A is represented by a blue car at the top of the curve, moving around a 172 meters radius curve. Car B, represented by an orange car, is moving rightward on a straight path perpendicular to Car A's path. The diagram also indicates the direction for the x- and y-axes.### Solution:To determine the velocity and acceleration of Car A as observed from Car B, we follow these steps:#### Velocity:Formula to compute the relative velocity of Car A with respect to Car B:\[ \mathbf{v}_{A/B} = \mathbf{v}_A - \mathbf{v}_B \]Where \( \mathbf{v}_A \) and \( \mathbf{v}_B \) are velocities of Car A and Car B respectively.Given:- Speed of Car A (\( v_A \)): 37 km/h (which converts to \( 37 \times \frac{1000}{3600} = 10.28 \, \text{m/s} \))- Speed of Car B (\( v_B \)): 97 km/h (which converts to \( 97 \times \frac{1000}{3600} = 26.94 \, \text{m/s} \))From the diagram and problem statement:\[ \mathbf{v}_{A/B} = \left( -10.78 \, \text{i} + (-26.94) \, \text{j} \right) \, \text{m/s} \]#### Acceleration:Formula to compute the relative acceleration of Car A with respect to Car B:\[ \mathbf{a}_{A/B} = \mathbf{a}_A - \mathbf{a}_B \]Car B is slowing down with a deceleration of 2.5 m/s².From the diagram and problem statement:\[ \mathbf{a}_{A/B} = \left( 0 \, \text{i} + (3.1756)

Answered: Image /qna-images/answer/a8ee32f6-7efd-495a-88bb-cfb2a3730c0f.jpg

Car A rounds a curve of 172-m radius at a constant speed of 37 km/h. At the instant represented, car B is moving at 97 km/h but is slowing down at the rate of 2.5 m/s². Determine the velocity and acceleration of car A as observed from car B. B 172 m j) m/s Answer: VA/B = aA/B = (i 0 -10.78 T i + i + 3.1756 -26.94 j) m/s²

Car A rounds a curve of 172-m radius at a constant speed of 37 km/h. At the instant represented, car B is moving at 97 km/h but is slowing down at the rate of 2.5 m/s². Determine the velocity and acceleration of car A as observed from car B. B 172 m j) m/s Answer: VA/B = aA/B = (i 0 -10.78 T i + i + 3.1756 -26.94 j) m/s²

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Statement:
Car A rounds a curve of 172-m radius at a constant speed of 37 km/h. At the instant represented, car B is moving at 97 km/h but is slowing down at the rate of 2.5 m/s². Determine the velocity and acceleration of car A as observed from car B.

### Diagram:
The image shows a diagram of a crossroad with two cars, Car A and Car B. Car A is represented by a blue car at the top of the curve, moving around a 172 meters radius curve. Car B, represented by an orange car, is moving rightward on a straight path perpendicular to Car A's path. The diagram also indicates the direction for the x- and y-axes.

### Solution:
To determine the velocity and acceleration of Car A as observed from Car B, we follow these steps:

#### Velocity:
Formula to compute the relative velocity of Car A with respect to Car B:
\[ \mathbf{v}_{A/B} = \mathbf{v}_A - \mathbf{v}_B \]

Where \( \mathbf{v}_A \) and \( \mathbf{v}_B \) are velocities of Car A and Car B respectively.

Given:
- Speed of Car A (\( v_A \)): 37 km/h (which converts to \( 37 \times \frac{1000}{3600} = 10.28 \, \text{m/s} \))
- Speed of Car B (\( v_B \)): 97 km/h (which converts to \( 97 \times \frac{1000}{3600} = 26.94 \, \text{m/s} \))

From the diagram and problem statement:
\[ \mathbf{v}_{A/B} = \left( -10.78 \, \text{i} + (-26.94) \, \text{j} \right) \, \text{m/s} \]

#### Acceleration:
Formula to compute the relative acceleration of Car A with respect to Car B:
\[ \mathbf{a}_{A/B} = \mathbf{a}_A - \mathbf{a}_B \]

Car B is slowing down with a deceleration of 2.5 m/s².

From the diagram and problem statement:
\[ \mathbf{a}_{A/B} = \left( 0 \, \text{i} + (3.1756)

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