The pilot of a plane measures an air velocity of 165km/h south relative to the plane. an observer on
the ground sees the plane pass overhead at a velocity of 145 km/h toward the north. what is the
velocity of the wind that is affecting the plane relative to the observer?

The speed obtained by the pilot is not accurate since it is measuring the rate of travel in the wind, true velocity is that compared to the ground. Therefore the speed of the wind is:

v wind = 165 - 145

v wind = 20 km/h

Therefore the wind velocity = 20 km/h against the plane.