A jet airliner is cruising at a speed of 510 miles per hour at a bearing of N16W. There is a 77 mph cross....?

Question

A jet airliner is cruising at a speed of 510 miles per hour at a bearing of N16W. There is a 77 mph crosswind striking it from a bearing of S42W. What is the resultant speed and course of the aircraft?

Answer 1

resultant velocity in the horizontal direction,
Vh=510*sin(16)-77sin(42)
resultant velocity in the vertical direction,
Vv=510cos(16)+77cos(42)
resultant velocity of the plane=sqrt(Vh^2 +Vv^2)
its direction=W tan^(-1)(Vv/Vh) N

Answer 2

The usual problem people have is with bearings. In terms of what you usually consider angles, the plane is on a 106 degree angle and the wind is blowing at an angle of 48 degrees. With the angles and trig, you can decompose both vectors to x and y components and construct the resultant with algebraic addition of the x and y components to determine angle and magnitude (phythag. thm.)