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The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N50°E. The wind is blowing from west to east at 40 miles per hour. The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind. Plane's speed: 180 miles per hour v + w 50° w Wind's speed: 40 miles per hour a. Express v and w in terms of their magnitudes and direction angles. b. Find the resultant vector, v + w. c. The magnitude of v + w, called the ground speed of the plane, gives its speed relative to the ground. Approximate the ground speed to the nearest mile per hour. d. The direction angle of v + w gives the plane's true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the plane's true bearing?

The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N50°E. The wind is blowing from west to east at 40 miles per hour. The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind. Plane's speed: 180 miles per hour v + w 50° w Wind's speed: 40 miles per hour a. Express v and w in terms of their magnitudes and direction angles. b. Find the resultant vector, v + w. c. The magnitude of v + w, called the ground speed of the plane, gives its speed relative to the ground. Approximate the ground speed to the nearest mile per hour. d. The direction angle of v + w gives the plane's true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the plane's true bearing?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 44E
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The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N50°E. The wind is blowing from west to east at 40 miles per hour. The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind. Plane's speed: 180 miles per hour v + w 50° w Wind's speed: 40 miles per hour a. Express v and w in terms of their magnitudes and direction angles. b. Find the resultant vector, v + w. c. The magnitude of v + w, called the ground speed of the plane, gives its speed relative to the ground. Approximate the ground speed to the nearest mile per hour. d. The direction angle of v + w gives the plane's true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the plane's true bearing?
Transcribed Image Text:The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N50°E. The wind is blowing from west to east at 40 miles per hour. The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind. Plane's speed: 180 miles per hour v + w 50° w Wind's speed: 40 miles per hour a. Express v and w in terms of their magnitudes and direction angles. b. Find the resultant vector, v + w. c. The magnitude of v + w, called the ground speed of the plane, gives its speed relative to the ground. Approximate the ground speed to the nearest mile per hour. d. The direction angle of v + w gives the plane's true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the plane's true bearing?
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