+185 an airplane travels with a speed of 145 miles hour in calm air. the wind is blowing with a velocity of 23 miles hour from N 27 degrees E.
a. if the plane is headed in a direction N 63 degrees W. Find the magnitude of the speed and the direction of the airplane with reference to the ground.
b. in what direction must the airplane ne headed in order to fly in the direction N 63 degrees W and what would be its actual speed in the air?
+128731 a. If the wind is blowing "from" N27E......its actual direction is 243° [ in terms of normal degree measure]
The plane is traveling in the intended direction of 153° [in terms of normal degree measure]
To get the the x ooordinate of resultant vector, we have
145cos153 + 23cos243 = -139.64
To get the y coordinate of the resulting vector, we have
145sin153 + 23sin243 = 45.36
So...the resuting magnitude = √[ (-139.64)^2 + (45.36)^2] = 146.8 mph
And the resulting direction =
arctan [ 45.36/-139.64] + 180° = 162° = N72W
