An jet is flying on a bearing of 38° at 420 miles per hour. Find the component form of the velocity of the Jet. Round your decimal to two places.
An jet is flying on a bearing of 38° at 420 miles per hour. Find the component form of the velocity of the Jet. Round your decimal to two places.
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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![### Problem Statement:
An educational question regarding vector components is displayed as follows:
**Question:**
An jet is flying on a bearing of 338° at 420 miles per hour. Find the component form of the velocity of the jet. Round your decimal to two places.
**Solution:**
To solve for the component form of the velocity of the jet, we need to break down the given velocity into its Cartesian components. The bearing of 338° is measured clockwise from the north.
1. **Convert the Bearing:**
The bearing of 338° can be converted to standard position angle from the positive x-axis (East):
- Standard position angle = 450° - bearing = 450° - 338° = 112°.
2. **Velocity Components (Vx and Vy):**
- Vx = V * cos(112°)
- Vy = V * sin(112°)
3. **Calculate the Components:**
Given V = 420 mph:
- Vx = 420 * cos(112°)
- Vy = 420 * sin(112°)
4. **Evaluate the Trigonometric Functions:**
Using trigonometric values:
- cos(112°) ≈ -0.3746
- sin(112°) ≈ 0.9272
5. **Final Calculations:**
- Vx = 420 * (-0.3746) ≈ -157.53 mph
- Vy = 420 * (0.9272) ≈ 389.42 mph
Thus, the component form of the velocity is approximately:
\[ \mathbf{V} = (-157.53 \, \text{mph}, 389.42 \, \text{mph}) \]
**Answer:**
The component form of the velocity of the jet is approximately \((-157.53, 389.42)\) when rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F666a7050-d460-4d4f-9624-d4bdba52f50b%2F1c92a4cb-6c23-4b2b-8709-0b56503bbc37%2Fo62jan_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
An educational question regarding vector components is displayed as follows:
**Question:**
An jet is flying on a bearing of 338° at 420 miles per hour. Find the component form of the velocity of the jet. Round your decimal to two places.
**Solution:**
To solve for the component form of the velocity of the jet, we need to break down the given velocity into its Cartesian components. The bearing of 338° is measured clockwise from the north.
1. **Convert the Bearing:**
The bearing of 338° can be converted to standard position angle from the positive x-axis (East):
- Standard position angle = 450° - bearing = 450° - 338° = 112°.
2. **Velocity Components (Vx and Vy):**
- Vx = V * cos(112°)
- Vy = V * sin(112°)
3. **Calculate the Components:**
Given V = 420 mph:
- Vx = 420 * cos(112°)
- Vy = 420 * sin(112°)
4. **Evaluate the Trigonometric Functions:**
Using trigonometric values:
- cos(112°) ≈ -0.3746
- sin(112°) ≈ 0.9272
5. **Final Calculations:**
- Vx = 420 * (-0.3746) ≈ -157.53 mph
- Vy = 420 * (0.9272) ≈ 389.42 mph
Thus, the component form of the velocity is approximately:
\[ \mathbf{V} = (-157.53 \, \text{mph}, 389.42 \, \text{mph}) \]
**Answer:**
The component form of the velocity of the jet is approximately \((-157.53, 389.42)\) when rounded to two decimal places.
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