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 :

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​