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 plane's velocity relative to the ground is the vector sum of its velocity relative to the air and the wind's velocity. Using the Pythagorean theorem, the resultant speed is √(156² + 20²) = 157 m/s. The angle south of east is calculated using tan⁻¹(20/156) = 7.31°.

A Plane Has an Eastward Heading at a Speed of 156