An airplane flies at airspeed (speed relative to
the air) 187 km/h. The pilot wishes to fly due
West but there is a 57.7 km/h wind blowing
in from North to South.
In what direction should the pilot head the
plane?
Answer in units of (north of West)

Question

An airplane flies at airspeed (speed relative to
the air) 187 km/h. The pilot wishes to fly due
West but there is a 57.7 km/h wind blowing
in from North to South.
In what direction should the pilot head the
plane?
Answer in units of  (north of West)

anonymous · Answer

What would be the ground speed of the plane
(its speed relative to the ground)?
Answer in units of km/h

anonymous · Answer

can you help on the question prior to this one... when your finished with this one.

anonymous · Answer

This is a little tricky. We can't fly due west because the wind will blow us off target to the south. Therefore, we must vectorize our flight such that our velocity to the north equals the velocity of the wind. The angle we are interested in is north of west. Let's draw a diagram. |dw:1327623668551:dw|$v_a$ is the velocity actually traveling west, $v_t$ is the velocity of the airplane, and $v_w$ is the velocity of the wind. 

From the diagram, we can see that $$v_a = v_t \cos(\theta)$$and$$v_w = v_t \sin(\theta)$$We know $v_w$ and $v_t$. Solve the second expression for $\theta$. The velocity of the airplane relative to the ground can be had from the first expression.