Calculating Airplane Velocity in Windy Conditions: A Vector Problem

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Homework Help Overview

The problem involves calculating the velocity of an airplane in windy conditions, specifically addressing how wind affects the airplane's path and speed. The context includes vector analysis, where the wind's speed and direction are given, along with the airplane's travel distance and time.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use the Pythagorean theorem and the law of sines for vector calculations but expresses uncertainty about their approach. Some participants question how to visualize the problem, particularly regarding the placement of vectors and the significance of the distance traveled. Others suggest breaking down the wind vector into components to analyze the airplane's velocity.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the use of vector components, but there is no explicit consensus on the best approach yet.

Contextual Notes

The original poster mentions a limited number of attempts remaining, which may influence their willingness to explore alternative methods. There is also a noted confusion regarding the problem's wording and the relationship between the various vectors involved.

tigerlili
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Homework Statement


After flying for 18 min in a wind blowing 49 km/h at an angle of 22° south of east, an airplane pilot is over a town that is 51 km due north of the starting point. What is the speed of the airplane relative to the air, in km/h?


Homework Equations



all i know to do here is to use the pythagorean theorem and maybe the law of sines to figure out the vectors

The Attempt at a Solution



i tried a couple of ways with different triangles but i only have 3 tries left and i seem to be floundering around in the dark on this one!
 
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Show us what you tried, then we will be able to correct and explain where you went wrong.
 
i honestly don't even know how to draw the diagram :/ i don't know where to put the starting point of the plane relative to the wind vector or what role the 51 km plays.. the wording is just confusing me
 
Alright, you know that the pilot has traveled 51 km in 18 minutes. You can use that information to find the pilot's velocity after wind resistance.

Wind is blowing at 49 km/h at an angle of 22 degrees south of east; find component vectors. You can then use the components to find the velocity before wind resistance. I think that's what's being asked.
 

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