A plane flies through wind that blows with a speed of 150 km/hr in the direction N 60° W. The plane has air speed of 500 km/hr and headed in the direction N 40° E. Determine the actual speed and direction of the plane. [T:3]
A plane flies through wind that blows with a speed of 150 km/hr in the direction N 60° W. The plane has air speed of 500 km/hr and headed in the direction N 40° E. Determine the actual speed and direction of the plane. [T:3]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
13
![**Problem 13:**
A plane flies through wind that blows with a speed of 150 km/hr in the direction N 60° W. The plane has an airspeed of 500 km/hr and is headed in the direction N 40° E. Determine the actual speed and direction of the plane.
**[T:3]**
**Analysis:**
To solve this problem, you can use vector addition. Represent the plane's velocity and the wind's velocity each as vectors and add these vectors to find the resultant vector, which represents the plane's actual velocity over the ground.
1. **Plane's Velocity Vector**:
- Magnitude: 500 km/hr
- Direction: N 40° E
2. **Wind's Velocity Vector**:
- Magnitude: 150 km/hr
- Direction: N 60° W
You will need to break these vectors into their north-south and east-west components. Once you have the components, add them to find the resultant vector. Then, calculate the magnitude and direction of this resultant vector to determine the plane's actual speed and course.
**Important Note:**
The description assumes basic knowledge of trigonometry and vector addition to perform the calculations necessary to find the resultant speed and direction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f85931-ed68-43c6-82f9-075f499bfced%2Ff63ff540-812f-4ea8-a0f8-97ba8b51e39c%2Fzylwll9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 13:**
A plane flies through wind that blows with a speed of 150 km/hr in the direction N 60° W. The plane has an airspeed of 500 km/hr and is headed in the direction N 40° E. Determine the actual speed and direction of the plane.
**[T:3]**
**Analysis:**
To solve this problem, you can use vector addition. Represent the plane's velocity and the wind's velocity each as vectors and add these vectors to find the resultant vector, which represents the plane's actual velocity over the ground.
1. **Plane's Velocity Vector**:
- Magnitude: 500 km/hr
- Direction: N 40° E
2. **Wind's Velocity Vector**:
- Magnitude: 150 km/hr
- Direction: N 60° W
You will need to break these vectors into their north-south and east-west components. Once you have the components, add them to find the resultant vector. Then, calculate the magnitude and direction of this resultant vector to determine the plane's actual speed and course.
**Important Note:**
The description assumes basic knowledge of trigonometry and vector addition to perform the calculations necessary to find the resultant speed and direction.
Expert Solution
Step 1
First break the components of both the speed in x and y directions and find their resultant.
Step by step
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