### Vector Problems in Airplane Navigation#### Problem 2.18:A plane flies for 3 hours and reaches a point 600 km north and 800 km east of its starting point. Find the direction and magnitude of its average velocity.#### Problem 2.19:A plane flies south at 500 km/h for 2 hours and then flies west at 500 km/h for 1 hour. 1. What is its average speed?2. What are the magnitude and direction of its average velocity?---### Solution Explanation:For Problem 2.18:- **Direction and Magnitude Calculation**: This involves using Pythagorean Theorem to calculate the magnitude of velocity vector and trigonometric functions to find the direction.For Problem 2.19:- **Average Speed Calculation**: This can be found by dividing the total distance traveled by the total time.- **Magnitude and Direction of Average Velocity**: This involves finding the resultant displacement vector and using it to calculate the average velocity. These problems help in understanding the concepts of vectors, magnitudes, and directions, crucial for navigation and related physics problems.

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2-18 A plane flies for 3 h and reaches a point 600 km north and 800 km east of its starting point. Find the direction and magnitude of its average velocity 2-19 A plane flies south at 500 km h¹ for 2 h and then flies west at 500 km h west for 1 h. (a) What is its average speed? (b) What are the mag- nitude and direction of its average velocity?

2-18 A plane flies for 3 h and reaches a point 600 km north and 800 km east of its starting point. Find the direction and magnitude of its average velocity 2-19 A plane flies south at 500 km h¹ for 2 h and then flies west at 500 km h west for 1 h. (a) What is its average speed? (b) What are the mag- nitude and direction of its average velocity?

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Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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Question

### Vector Problems in Airplane Navigation

#### Problem 2.18:
A plane flies for 3 hours and reaches a point 600 km north and 800 km east of its starting point. Find the direction and magnitude of its average velocity.

#### Problem 2.19:
A plane flies south at 500 km/h for 2 hours and then flies west at 500 km/h for 1 hour.

1. What is its average speed?
2. What are the magnitude and direction of its average velocity?

---

### Solution Explanation:

For Problem 2.18:
- **Direction and Magnitude Calculation**: This involves using Pythagorean Theorem to calculate the magnitude of velocity vector and trigonometric functions to find the direction.

For Problem 2.19:
- **Average Speed Calculation**: This can be found by dividing the total distance traveled by the total time.
- **Magnitude and Direction of Average Velocity**: This involves finding the resultant displacement vector and using it to calculate the average velocity.

These problems help in understanding the concepts of vectors, magnitudes, and directions, crucial for navigation and related physics problems.

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