Apilot with an airspeed (speed with respect to air) of 120 km/hr wishes to fly due north. a 40 km/h wind is blowing from the northeast. in what direction should she head and what will her ground speed be (speed with respect to the ground)?

Let denote the vector for velocity of the plane relative to the ground, and the corresponding speed. The pilot wants to be heading due north, taking the effect of the wind into account, so that this vector has components

The wind (denoted by for air) is blowing from the northeast, which means its direction is southwest, so that the vector for its velocity relative to the ground is

The plane has an airspeed of 120 km/h, but its direction is unknown, so the vector for its velocity relative to the air is

We have

The components tell us that we should have

(both relative to east) By drawing a diagram like the one attached, you'll see that the smaller angle is the correct choice. Then by matching the components, we can solve for :

current and voltage can both be different in different parts of a circuit so it matters where you place the ammeter and voltmete