calculus
posted by Sam .
An airplane is flying at 550 km/h on a heading of 080 degrees. The wind is blowing at 60 km/h from a bearing of 120 degrees. Find the ground velocity of the airplane and include the new bearing.

This is not calculus.
The air (wind) velocity PLUS the plane's air velocity equals the ground velocity.
Perform the vector addition 
Vpw = Vp + Vw = 550[80o] + 60[120o] =
550*cos80+550*sin80 +60*Cos120+60*sin120
= 95.5+541.6i  30+52i = 65.5 + 593.6i.
= 597mi/h[83.7o]. 
Note: Vpw = 597km/h[83.7o] E. of N.