Solving Plane Velocity Relative to Ground: Homework Help

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To find the speed of the airplane relative to the ground, the velocities must be combined vectorially since they are perpendicular. The airplane's velocity is 189 m/s west, and the wind's velocity is 50 m/s north. Using the Pythagorean theorem, the correct calculation involves finding the resultant vector: speed relative to ground = √(189² + 50²), which equals approximately 199.5 m/s. The initial assumption of simply adding the speeds was incorrect due to the need for vector addition. Understanding the concept of relative velocity is crucial in solving such problems accurately.
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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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