An airplane is flying at a velocity of 300km/h S30degrees W in a wind blowing at a velocity of 50km/h S20degrees E. What is the true speed and direction of plane?

Answer 1

converting your directions to standard trig notation
(x-axis is zero, counterclockwise)

S 30° W ----> 240°
S 20° E ----> 290°

300 km/h in S30W ---> vector(400cos240,400sin240)
50 km/h in S20E --> vector (50cos290 , 50sin 290)

resultant = (400cos240 + 50cos290 , 400sin240+50sin290)
= appr (-246.98, -393.339)

magnitude = √( (-246.98)^2 + (-393.339)^2)
= appr 464.5 km/h

direction:
tanØ = -393.339/-246.98) , Ø in III
Ø = appr 180 + 57.9 or 237.9°
or S 32.1° W