The captain of a small plane starts his journey by proceeding east. The spee km/h. A sudden north wind starts to blow at a constant speed of 71.0 km/h he ground if no action is taken by the pilot? £60
The captain of a small plane starts his journey by proceeding east. The spee km/h. A sudden north wind starts to blow at a constant speed of 71.0 km/h he ground if no action is taken by the pilot? £60
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: Determining Plane Speed Relative to Ground**
The captain of a small plane starts his journey by proceeding east. The speed of the plane with respect to still air is 160 km/h. A sudden north wind starts to blow at a constant speed of 71.0 km/h. What is the speed of the plane relative to the ground if no action is taken by the pilot?
**Answer:**
To find the speed of the plane relative to the ground, we need to use vector addition to combine the speed of the plane and the speed of the wind.
- The plane's velocity with respect to still air is 160 km/h east.
- The wind's velocity is 71.0 km/h north.
Since these two vectors are perpendicular to each other (east and north), we can use the Pythagorean theorem to find the resultant speed \( V_r \) of the plane relative to the ground.
The formula to find the resultant speed is:
\[ V_r = \sqrt{(V_{\text{plane}}^2 + V_{\text{wind}}^2)} \]
Where:
- \( V_{\text{plane}} \) is the speed of the plane with respect to still air.
- \( V_{\text{wind}} \) is the speed of the wind.
Plugging in the given values:
\[ V_r = \sqrt{(160^2 + 71^2)} \]
\[ V_r = \sqrt{(25600 + 5041)} \]
\[ V_r = \sqrt{30641} \]
\[ V_r \approx 175 km/h \]
Therefore, the speed of the plane relative to the ground is approximately 175 km/h.
**Answer: 175 km/h**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88cd9656-9419-481b-bc0b-e9aadd0312cb%2Fc0de3897-1ed7-46ec-ac8c-31b07d44e624%2F1y70cdt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 10: Determining Plane Speed Relative to Ground**
The captain of a small plane starts his journey by proceeding east. The speed of the plane with respect to still air is 160 km/h. A sudden north wind starts to blow at a constant speed of 71.0 km/h. What is the speed of the plane relative to the ground if no action is taken by the pilot?
**Answer:**
To find the speed of the plane relative to the ground, we need to use vector addition to combine the speed of the plane and the speed of the wind.
- The plane's velocity with respect to still air is 160 km/h east.
- The wind's velocity is 71.0 km/h north.
Since these two vectors are perpendicular to each other (east and north), we can use the Pythagorean theorem to find the resultant speed \( V_r \) of the plane relative to the ground.
The formula to find the resultant speed is:
\[ V_r = \sqrt{(V_{\text{plane}}^2 + V_{\text{wind}}^2)} \]
Where:
- \( V_{\text{plane}} \) is the speed of the plane with respect to still air.
- \( V_{\text{wind}} \) is the speed of the wind.
Plugging in the given values:
\[ V_r = \sqrt{(160^2 + 71^2)} \]
\[ V_r = \sqrt{(25600 + 5041)} \]
\[ V_r = \sqrt{30641} \]
\[ V_r \approx 175 km/h \]
Therefore, the speed of the plane relative to the ground is approximately 175 km/h.
**Answer: 175 km/h**
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