
Vector problem
A plane flying due east at 200 km/hour encounters as a 40 km/hour northeasterly wind. The resultant velocity of the plane is the vector sum v = v1 + v2, where v1 is the velocity vector of the plane and v2 is the velocity vector of the wind. The angle between both vectors is pi/4. Determine the resultant speed of the plane (the length of v).
I don't like vectors. Maybe they don't like me either.
Dang, this whole chapters on vectors. =(
I miss integrals.

law of cosines will get it quickly ...
$\displaystyle v = \sqrt{v_1^2 + v_2^2  2v_1v_2\cos\left(\frac{\pi}{4}\right)}$

For the first part under the square root, does that mean the exponent of v2 divided by the exponent of v1?

it means $\displaystyle v_1$ squared + $\displaystyle v_2$ squared