Solving Plane Velocity Relative to Ground: Homework Help

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SUMMARY

The problem involves calculating the velocity of an airplane relative to the ground, given its velocity relative to the air and the wind's velocity. The airplane's velocity is 189 m/s westward, while the wind's velocity is 50 m/s northward. The correct approach to find the ground speed is to use vector addition, specifically the Pythagorean theorem, since the velocities are perpendicular. The resultant speed of the plane relative to the ground is approximately 193.5 m/s at an angle northwest.

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Homework Statement


An airplane has a velocity relative to the air of 189 m/s in a westerly direction. If the wind has a speed relative to the ground of 50 m/s directed to the north, what is the speed of the plane relative to the ground?


Homework Equations


I'm not entirely sure..


The Attempt at a Solution


I figured speed of plane relative to the ground = speed of plane relative to the air + speed of air relative to ground.
So I put in x=189+50
Our homeworks are put online, and I already found out this answer was wrong.

If anyone could help that'd be great! thanks!
 
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I would just add them vectorially, were the plane's velocity relative to the ground.. I'm not sure what they mean exactly by relative to the air, considering the vectors are perpendicular.
 

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