Question

An airplane is traveling due east with a velocity of 583 miles per hour. The wind blows at 75 miles per hour at an angle of S58°. What is the resultant speed and direction of the plane?
A. 650.5 miles per hour; S7.8°E
B. 626.0 miles per hour; S84.2°E
C. 653.6 miles per hour; S3.5°E
D. 647.8 miles per hour; S86.5°E

Answer 1

Answer:

  D. 647.8 miles per hour; S86.5°E

Step-by-step explanation:

We assume the wind direction is supposed to be S58°E. Then the bearing of the plane measured clockwise from north is 90°, and the direction the wind is blowing toward has a bearing of 122°. The resultant speed and direction is the sum of the two vectors, which is easily found using a suitable calculator:

  583∠90° + 75∠122° = 647.8∠93.5°

The bearing of 93.5° translates to the direction S86.5°E.

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An angle east of south is subtracted from 180° (south) to find the equivalent bearing.