# Finding a plane's heading and length of trip

• May 25th 2010, 04:40 PM
RyGuy
Finding a plane's heading and length of trip
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?
• May 25th 2010, 04:54 PM
skeeter
Quote:

Originally Posted by 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?

I take it that you've made a sketch of the Air + Wind = Ground velocity vectors ...

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

$\theta$ = heading angle relative to east

using components ...

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

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

from the second equation ...

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

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

$G \approx 595$ km/hr

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