a plane takes off heading west at a ground velocityof 500kph and climbing at an angle of 8 degrees. A 15kph wind is blowing from the north. Determine the resultant air and ground velocities (sketch and label a diagram)

Question

zehanz · Answer

Here is a start:

anonymous · Answer

ok but can u draw a simple diagram please

zehanz · Answer

It is a 3d-situation, so a diagram is not that easy.
I've tried to make simplified diagrams (top view and side view).
The length of the green vector (495.36 km/h) is the ground speed (used Pythagorean Theorem).
The length of the red vector (500.22 km/h) is the airspeed (imo).

zehanz · Answer

Calculating angles could also easily done with the diagrams...

anonymous · Answer

what i did was use the cosine law to find the resultant: r^2=(15)^2+(500)^2-2*15*500cos 88

anonymous · Answer

is this right?

zehanz · Answer

No, I don't think so.
Because the wind is perpendicular to the direction the plane is going, you must use the Pythagorean Theorem to find the resultant. See my drawings.
Furthermore, while the wind adds to the speed, your calculation leads to a lower speed. (about 485 km/h).