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A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 20.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity?.

A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 20.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity?.

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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6. Always begin by writing the general form of an equation. Insert numbers and units. Remember to show all work (and units). Present  the solution well organized and clearly.

answer should be: |???⃗⃗⃗⃗⃗⃗|=185??/ℎ,?=22.3°,????ℎ ?? ????

just need an explanation on how to get to this.

**Problem 6:** A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 20.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity? **Explanation:** When solving this problem, consider the following: - The airspeed of the plane is the speed at which it moves relative to the air. It has to account for both the wind speed and direction changes to maintain a course effectively. - The wind velocity will alter the plane’s effective ground speed and course. - By knowing the time and distance, you can calculate the plane's ground velocity. - The vector addition (or diagram) involves three vectors: the airspeed vector, the wind velocity vector, and the ground velocity vector. To find the answer, calculations would involve using trigonometry to solve for the wind velocity vector's magnitude and direction relative to the ground velocity vector.
Transcribed Image Text:**Problem 6:** A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 20.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity? **Explanation:** When solving this problem, consider the following: - The airspeed of the plane is the speed at which it moves relative to the air. It has to account for both the wind speed and direction changes to maintain a course effectively. - The wind velocity will alter the plane’s effective ground speed and course. - By knowing the time and distance, you can calculate the plane's ground velocity. - The vector addition (or diagram) involves three vectors: the airspeed vector, the wind velocity vector, and the ground velocity vector. To find the answer, calculations would involve using trigonometry to solve for the wind velocity vector's magnitude and direction relative to the ground velocity vector.
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