**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**

GivenSpeed of the plane with respect to still air in east direction, vP→=160 i^ km/hSpeed of wind in…

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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Concept explainers

Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.

Question

**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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