Airplane Velocity: 151.97 km/h NW

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Homework Help Overview

The problem involves determining the resultant velocity of an airplane flying due west with a given speed, while also considering the effect of a northward wind. The subject area pertains to vector addition and trigonometry in the context of physics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of the airplane's resultant speed and direction, with one participant attempting to use the Pythagorean theorem for magnitude and trigonometric functions for direction. Questions arise regarding the correct interpretation of angles in relation to compass directions.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the angle measurement and the implications of compass directions versus mathematical angles. Some guidance has been offered regarding the distinction between these systems, but no consensus has been reached.

Contextual Notes

There is a noted confusion regarding the quadrant placement of the resultant vector and how angles are measured from the west in this context. Participants are also considering the implications of the wind's direction on the airplane's velocity vector.

waldvocm
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An airplane is heading due west. The airplane's speed relative to the air is 150.0 km/h. If there is a wind of 24.4km/h toward the north, what is a) the magnitude (km/h)

I used the equation sqrt 150.0^2+24.4^2 =151.97

b)what is the direction (degrees measured from west) of the velocity of the plane relative to the ground?

tan-1(24.4/150.0)=9.23 Would you add 90degrees to this =99.23
 
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Well since the wind is north and the plane is heading due west, it must be within 270 and 360 degrees (on a compass).
 
I don't understand that.

Since it is heading due west, which would be on the -x axis. And the wind is blowing north wouldn't the angle be in the 2nd quadrant relative to the ground. Which would place the vector in the second quadrant between 90 and 180 degrees?

Can you elaborate on your previous response?
 
The question asks for "degrees measured from west". I would answet it as "9.23 degrees north of west"

Compass courses differ from the angles that are used in mathematics N 0, E 90, S 180, W 270.
 

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