An airplane is flying at a speed of 520 miles per hour at an angle of 30°. At one point during flight, the plane comes across a wind with a velocity of 50 miles per hour at an angle of 15°. Find the resulting direction and speed of the airplane.
+129839 We have two vectors
(520 cos 30, 520 sin30) and (50cos 15, 50 sin15)
x value of resultant vector =
520cos30 + 50 cos15 ≈ 498.63 mph
y value of resultant vector =
520 sin 30 + 50sin 15 ≈ 272.94 mph
Resultant speed = √[ 498.63^2 + 272.94^2 ] ≈ 568.4 mph
Resultant angle =
arctan ( 272.94/498.63) = θ = 28.7°
