A plane is heading due south at 200 mph. The wind is blowing S30°W at 25 mph. Find the ground speed of the plane and resulting direction of the plane.

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