A plane is heading due east (its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind) while climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 490 km/h and there is a wind blowing 80 km/h to the northwest, what is the ground speed of the plane?

Use V to denote the plane speed vector with respect to Earth, Vair to denote the air speed vector, and W to denote the wind speed vector. Start by writing a relationship between these three velocity vectors, and write their components (known and unknown). Use the available information to determined the unknowns.