SOLUTION: A plane is heading due south with an airspeed of 288 mph. A wind from a direction of 58� is blowing at 20 mph. Find the bearing of the plane.

Question 814549: A plane is heading due south with an airspeed of 288 mph. A wind from a direction of 58� is blowing at 20 mph. Find the bearing of the plane.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
use vector addition:
---
wind vector w:
direction from = 58 degrees
direction to = 238 degrees
magnitude = 20
---
decompose w into rectangular coordinates:
wy = 20cos(58) = 10.598
wx = 20sin(58) = 16.961
---
airplane vector a:
direction = 180 degrees
magnitude = 288
---
decompose a into rectangular coordinates:
ay = 288cos(0) = 288
ax = 288sin(0) = 0
---
sum:
sy = ay + wy = 288 + 10.598 = 298.598
sx = ax + wx = 0 + 16.961 = 16.961
---
convert the sum vector to polar form:
s = sqrt( sx^2 + sy^2 ) = 299.079 mph
t = arctan( sx / sy ) = 3.251 degrees
---
Answer:
the airplane will fly a bearing of (180 + 3.251) = 183.251 degrees at a ground speed of 299.079 mph
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