The velocity of an airplane heading east is 400 knots with a wind velocity of 50 knots blowing toward the northeast. calculate the resultant speed and direction of the plane. round to the nearest tenth.

1. To Calculate the resultant speed of the plane, you need to find the speed of the air, add it to the plane speed, then find the resultant using trigonometry.

The velocity of the plane:
east=400 knots

The velocity of the air
50knots north east = 50/√2 north + 50/√2 east

The resultant speed would be:
total speed^2= east^2 + north^2
total speed= √(400+50/√2)^2 + (50/√2)^2
total speed= √(189534.254 + 1250)
total speed= 436.8 knots

2. To count the direction of the plane, you need to find the total speed of x(east/west) and y(north/south) axis separately then use tan formula.
east speed= 400knots + 50/√2 knots= 435.35 knots
north speed= 50/√2knots= 35.35 knots

tan a= opposite/adjacent
tan a = north speed/ east speed
tan a= 35.35/ 435.35 
tan a=0.0812
a= 4.6 degrees