Relative velocity: A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while 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 (20.0 m/s) form a right-angled triangle. The magnitude of the resultant velocity (relative to the ground) is $\sqrt{156^2 + 20^2} = 157$ m/s. The angle $\theta$ south of east is given by $\tan^{-1}(20/156) = 7.31^\circ$.

Relative Velocity: a Plane Has an Eastward Heading at a Speed