Aplane 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 degreesdirection to = 238 degreesmagnitude = 20decompose w into rectangular coordinates: wy = 20cos(58) = 10.598wx = 20sin(58) = 16.961airplane vector a: direction = 180 degreesmagnitude = 288decompose a into rectangular coordinates: ay = 288cos(0) = 288ax = 288sin(0) = 0sum: sy = ay + wy = 288 + 10.598 = 298.598sx = ax + wx = 0 + 16.961 = 16.961convert the sum vector to polar form: s = sqrt( sx^2 + sy^2 ) = 299.079 mpht = arctan( sx / sy ) = 3.251 degreesanswer: the airplane will fly a bearing of (180 + 3.251) = 183.251 degrees at a ground speed of 299.079 mph