An airplane is flying on a compass heading (bearing) of 170 at 460 mph. A wind is blowing with the bearing 200 at 80 mph.

a. Find the component form of the velocity of the airplane.

b. Find the actual ground speed and direction of the airplane

Answer:

a. v = 460 = < -453.01, 79.88 >

b. Find the wind vector w = 80 = <-75.18, -27.36>

Velocity vector = v + w = < -528.19, 52.52>

Actual speed ||v + w||sqrt[(-528.19)^2+(52.52)^2] = 530.79mph (nearest hundredth)

Actual direction: =180 degrees +tan^-1(-528.19/52.52)= 95.68