A plane has an eastward heading with an airspeed of 156 m/s.A 20.0 m/s wind is blowing southward at the same time as the plane is flying.The velocity of the plane relative to the ground is
A)157 m/s at an angle 7.31° south of east.
B)157 m/s at an angle 7.31° east of south.
C)155 m/s at an angle 7.36° south of east.
D)155 m/s at an angle 7.36° east of south.
E)157 m/s at an angle 7.36° south of east.

Question

Quizplus · Accepted Answer

The velocity of the plane relative to the ground can be found using vector addition. The eastward velocity (156 m/s) and the southward wind velocity (20 m/s) form a right-angled triangle. The magnitude of the resultant velocity (ground speed) is $\sqrt{156^2 + 20^2} = 157$ m/s. The angle $\theta$ south of east is given by $\tan^{-1}(20/156) = 7.31^\circ$.

A Plane Has an Eastward Heading with an Airspeed of 156