Velocity of Plane Relative to Ground: Answer & Explanation

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The discussion focuses on calculating the velocity of a plane moving eastward at 210 km/hr while experiencing a southward wind of 85.0 km/hr. The resultant velocity is determined to be 227 km/hr. The angle of this velocity, calculated using the tangent function, is 22 degrees. The confusion arises regarding the directional terminology, specifically whether the angle is described as south of east or east of south.

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A plane is headed eastward at a speed of 210 km/hr. The wind is blowing southward at 85.0 km/hr. The velocity of the plane relative to the ground is?
a. 192 km/hr at an angle of 22 degrees south of east
b. 192 km/hr at an angle of 22 degrees east of south
c. 227 km/hr at an angle of 68 degrees south of east
d. 227 km/hr at an angle of 68 degrees east of south

For the velocity, I did square root (210^2 + 85.0^2) and I got 227 km/hr. However, when finding the angle, I did tan-1(85/210) and got 22 degrees. I don't know which one would be the correct answer then.
 
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First tell me,

Which direction does tan-1(85/225) signify-
east of south or south of east?

The answer to your question lies in this particular answer!
 
Hi,

Agree with you.. please justify the direction..
 

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