**Problem 11:**A plane flying for 20 minutes in a 40 km/h wind blowing towards 25° south of east is over a town that is 50 km due north of the airport where it took off from.(a) What is the ground speed of the airplane including direction?(b) What is the air speed of the airplane including direction?(c) Include a diagram of the situation.**Explanation:**For this problem, it is necessary to analyze the vectors involved in the airplane's flight. The wind is influencing the plane's path, and both the airplane's airspeed and the wind speed affect its actual path over the ground (ground speed).1. **Vector Analysis:** - The wind vector is 40 km/h towards 25° south of east. - The displacement vector from the airport to the town is 50 km due north. - The time of flight is 20 minutes, which is 1/3 of an hour.2. **Calculations:** - Use vector addition to calculate the airplane's ground speed and direction. - Determine the airplane's airspeed by considering the vector components.3. **Diagram:** - A diagram would typically show: - A line representing the path from the airport to the town (50 km north). - A vector representing the wind direction (40 km/h, 25° south of east). - The resultant vector representing the airplane's path relative to the ground.

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Description: **Problem 11:**A plane flying for 20 minutes in a 40 km/h wind blowing towards 25° south of east is over a town that is 50 km due north of the airport where it took off from.(a) What is the ground speed of the airplane including direction?(b) What i

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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 11:**

A plane flying for 20 minutes in a 40 km/h wind blowing towards 25° south of east is over a town that is 50 km due north of the airport where it took off from.

(a) What is the ground speed of the airplane including direction?

(b) What is the air speed of the airplane including direction?

(c) Include a diagram of the situation.

**Explanation:**

For this problem, it is necessary to analyze the vectors involved in the airplane's flight. The wind is influencing the plane's path, and both the airplane's airspeed and the wind speed affect its actual path over the ground (ground speed).

1. **Vector Analysis:**
- The wind vector is 40 km/h towards 25° south of east.
- The displacement vector from the airport to the town is 50 km due north.
- The time of flight is 20 minutes, which is 1/3 of an hour.

2. **Calculations:**
- Use vector addition to calculate the airplane's ground speed and direction.
- Determine the airplane's airspeed by considering the vector components.

3. **Diagram:**
- A diagram would typically show:
- A line representing the path from the airport to the town (50 km north).
- A vector representing the wind direction (40 km/h, 25° south of east).
- The resultant vector representing the airplane's path relative to the ground.

Expert Solution

Step 1: Wrte given values

Consider $stack v subscript A with rightwards arrow on top$ and $stack v subscript G with rightwards arrow on top$ be the velocity of the plane with respect to air and ground respectively.

Let the east be towards the positive x-axis and the north be towards the positive y-axis.

plane covered $d equals 50 space km$ in $t equals 20 space min equals 20 over 60 straight h equals 1 third straight h$ .

The wind velocity is

$v with rightwards arrow on top subscript w equals 40 cos 25 degree space ı with hat on top minus 40 sin 25 degree space ȷ with hat on top$

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