An airplane is flying at a bearing of $143 ^ { \circ }$ with an airspeed of 335 kilometers per hour. Because of the wind, its ground speed and direction are, respectively, 325 kilometers per hour and $138 ^ { \circ }$. Find the direction and speed of the wind. Round your answer to two decimals.
A) $31.36 ^ { \circ } , 30.47$ kilometers per hour
B) $121.36 ^ { \circ } , 25.71$ kilometers per hour
C) $- 37.01 ^ { \circ } , 30.47$ kilometers per hour
D) $31.36 ^ { \circ } , 25.71$ kilometers per hour
E) $121.36 ^ { \circ } , 25.69$ kilometers per hour

Question

Quizplus · Accepted Answer

To solve this, we use vector addition, where the airplane's velocity vector and the wind's velocity vector add up to the resultant ground velocity vector. Given the airplane's airspeed and bearing, and its ground speed and direction, we can calculate the wind's speed and direction by decomposing the vectors into their north-south and east-west components and then solving for the wind's components. The correct calculation leads to a wind direction of $31.36^\circ$ and a speed of $30.47$ kilometers per hour.

An Airplane Is Flying at a Bearing Of 143∘143 ^ { \circ }143∘

An Airplane Is Flying at a Bearing Of $143 ^ { \circ }$