# Finding a plane's heading and length of trip

#### RyGuy

The pilot of an airplane that flies at 650 km/h wishes to travel to a city 1000 km due east. There is a 75 km/h wind from the northeast.

a)What should the plane's heading be?

b) How long will the trip take?

#### skeeter

MHF Helper
The pilot of an airplane that flies at 650 km/h wishes to travel to a city 1000 km due east. There is a 75 km/h wind from the northeast.

a)What should the plane's heading be?

b) How long will the trip take?
I take it that you've made a sketch of the Air + Wind = Ground velocity vectors ...

let $$\displaystyle G$$ = groundspeed along a track due east.

$$\displaystyle \theta$$ = heading angle relative to east

using components ...

$$\displaystyle 650\cos{\theta} - 75\cos(45) = G$$

$$\displaystyle 650\sin{\theta} - 75\sin(45) = 0$$

from the second equation ...

$$\displaystyle \theta = \arcsin\left[\frac{75\sin(45)}{650}\right] \approx 4.7^\circ$$

plane should steer about $$\displaystyle 5^\circ$$ north of east.

$$\displaystyle G \approx 595$$ km/hr

... this problem can also be completed using the law of cosines.