Calculating Airplane Velocity and Direction with Wind

[Canesfanatic]

Hi, this is my first time posting here, and i was working out this physics problem and it occurred to me that when i calculated the velocity of an airplane in my problem, it's higher than the speed of the airplane...i know i probably didn't explain that too well, so here goes:

the problem:
The pilot of an aircraft wishes to fly due west in 50.0 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 205 km/hr.
a. In what direction should the aircraft head?
on this, I set up a right triangle with the velocities as vectors and calculated that the aircraft should fly 13.7 degrees north of west using angle=tan^-1 * (50.0 km/h/205km/h

b. What should its speed be relative to the ground?
Again, on this I set up another right triangle, and when i calculated the answer, it came up as 211. km/hr. I used the pythagorean theorum with (50.0km/h)^2+(205km/h)^2= C^2

What I am not sure about is whether I went about this problem with the right approach and whether 211. km/hr is the correct answer for B. All help is appreciated

 

[Doc Al]

a. In what direction should the aircraft head?
on this, I set up a right triangle with the velocities as vectors and calculated that the aircraft should fly 13.7 degrees north of west using angle=tan^-1 * (50.0 km/h/205km/h

This isn't quite right. You need to add these vectors: (1) The velocity of the plane with respect to the air + (2) the velocity of the air with respect to the ground. This gives you the resultant velocity of the plane with respect to the ground--which you know must point west. So you need to find what direction (1) must point so that the resultant is purely to the west. You know the magnitude of (1), now find the direction.

Draw yourself a diagram: Start by drawing vector (2). Then play around with vector (1) until you see where it must point--then use a little trig to find the angle.