Finding a plane's heading and length of trip

Nov 2009
6
0
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
Jun 2008
16,217
6,765
North Texas
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.