Question

a plane is heading 60 degrees east of south at 180 km/hr. a 50 km/hr wind blows in the direction of 25 degrees west of south. find the resultant velocity and bearing.

Answer 1

Make a reasonable sketch.
Using vectors and using R to be the resultant vector:

R = (180cos300,180sin300) + (50cos245,50sin245)
= (90,-90√3) + (-21.1309.. , -45.31538..)
= (68.869.., -201.1996...)

Magnitude = √(68.869^2 + (-201.1996..)^2)
= appr 212.66 km

direction:
tanØ = -201.1996/68.869
= ..
Ø = 360-71.104
= appr 288.9°

check my arithmetic