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10. A pilot wants her bearing to be 70° and her groundspeed to be 325 mph. There is a 45 mph wind blowing from 230°. What bearing should she take? What will her airspeed be? Round the speed to the nearest mph and the bearing to the nearest minute.

10. A pilot wants her bearing to be 70° and her groundspeed to be 325 mph. There is a 45 mph wind blowing from 230°. What bearing should she take? What will her airspeed be? Round the speed to the nearest mph and the bearing to the nearest minute.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 10:** A pilot wants her bearing to be \(70^\circ\) and her groundspeed to be 325 mph. There is a 45 mph wind blowing from \(230^\circ\). What bearing should she take? What will her airspeed be? Round the speed to the nearest mph and the bearing to the nearest minute. **Solution:** To solve this problem, we will utilize vector diagrams and trigonometry to determine the resultant bearing and airspeed of the pilot. 1. **Understanding the Given Data**: - Desired bearing: \(70^\circ\) - Groundspeed: 325 mph - Wind speed: 45 mph - Wind direction: \(230^\circ\) 2. **Diagram Setup**: - The direction \(230^\circ\) from north corresponds to approximately south-west. Using vector subtraction, we determine the required course (or airspeed direction) to achieve the desired groundspeed \(70^\circ\). 3. **Vector Calculation using Trigonometry**: - To solve, we set up the vectors. - Compute the x and y components of the wind vector. - Adjust pilot’s course to compensate for wind impact. 4. **Result**: - **Bearing**: Calculated using the vector addition method and corrected to the nearest minute. - **Airspeed**: Calculated and rounded to the nearest mph. This vector calculation involves decomposing the wind and pilot’s velocity vectors into components, applying necessary adjustments, and reforming the resultant vector to find desired parameters.
Transcribed Image Text:**Problem 10:** A pilot wants her bearing to be \(70^\circ\) and her groundspeed to be 325 mph. There is a 45 mph wind blowing from \(230^\circ\). What bearing should she take? What will her airspeed be? Round the speed to the nearest mph and the bearing to the nearest minute. **Solution:** To solve this problem, we will utilize vector diagrams and trigonometry to determine the resultant bearing and airspeed of the pilot. 1. **Understanding the Given Data**: - Desired bearing: \(70^\circ\) - Groundspeed: 325 mph - Wind speed: 45 mph - Wind direction: \(230^\circ\) 2. **Diagram Setup**: - The direction \(230^\circ\) from north corresponds to approximately south-west. Using vector subtraction, we determine the required course (or airspeed direction) to achieve the desired groundspeed \(70^\circ\). 3. **Vector Calculation using Trigonometry**: - To solve, we set up the vectors. - Compute the x and y components of the wind vector. - Adjust pilot’s course to compensate for wind impact. 4. **Result**: - **Bearing**: Calculated using the vector addition method and corrected to the nearest minute. - **Airspeed**: Calculated and rounded to the nearest mph. This vector calculation involves decomposing the wind and pilot’s velocity vectors into components, applying necessary adjustments, and reforming the resultant vector to find desired parameters.
Expert Solution
Step 1

Given information:

Physics homework question answer, step 1, image 1

Here, θb and θw are the angles of bearing and wind direction respectively, vp and vw are the speed of the plane and the wind respectively.

Step 2

The situation is represented in the diagram below.

Physics homework question answer, step 2, image 1

Step 3

The vector vp­ in the component form can be represented as,

Physics homework question answer, step 3, image 1And the vector vw­ in the component form can be represented as,

Physics homework question answer, step 3, image 2

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