Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 6, Problem 60RE
To determine

To find: The resultant speed and the direction of the plane.

Expert Solution & Answer
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Answer to Problem 60RE

The resultant speed is 422.3 miles/h and the direction of the plane is 45° .

Explanation of Solution

Given information:

The speed of the airplane is 430 miles/h and the speed of the wind is 35 miles/h

Consider the velocity diagram of the airplane and the wind:

  Precalculus with Limits: A Graphing Approach, Chapter 6, Problem 60RE

The resultant speed is calculated as,

  V=‖a‖2+‖b‖2+2‖a‖‖b‖cosθ=(430)2+(35)2+2(430)(35)cos(135°−30°)=422.3 miles/h

The direction of the plane is calculated as,

  θ=tan−1(135sin105°35+135cos105°)θ=89.97°ϕ=89.97°−(135°−90°)ϕ≈45°

Therefore, the resultant speed is 422.3 miles/h and the direction of the plane is 45°

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Chapter 6, Problem 59RE
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Chapter 6, Problem 61RE

Chapter 6 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
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