# Airplane vectors

• Feb 16th 2011, 02:26 PM
Barthayn
Airplane vectors
12. A pilot wishes to fly from Toronto to Montreal, a distance of 508 km on a bearing of 075^o. The cruising speed of the plane is 550 km/h. An 80 km/h wind is blowing on a bearing of 125^o

a) What heading should the pilot take to reach his destination?
b) What will be the speed of the plane relative to the ground?
c) How long will the trip take?

I do not know how to get the angle the pilot should take. I don't understand how to do it. I know there is a little angle of 15^o, however, can't find the angle in the triangle to add to the little angle then subtract it from 90^o. I know this is easy, however, can't seem find the method to find the bearing.

NOTE: All angles are from true North [up] and then rotate clockwise.
• Feb 16th 2011, 03:44 PM
skeeter
Quote:

Originally Posted by Barthayn
12. A pilot wishes to fly from Toronto to Montreal, a distance of 508 km on a bearing of 075^o. The cruising speed of the plane is 550 km/h. An 80 km/h wind is blowing on a bearing of 125^o

a) What heading should the pilot take to reach his destination?
b) What will be the speed of the plane relative to the ground?
c) How long will the trip take?

NOTE: All angles are from true North [up] and then rotate clockwise.

law of cosines ...

$\displaystyle A^2 = G^2 + W^2 - 2GW \cos(50^\circ)$

$\displaystyle 550^2 = G^2 + 80^2 - 160G\cos(50^\circ)$

solve the resulting quadratic for $\displaystyle G$ , the Ground speed.

Once you find $\displaystyle G$ , calculate the time to travel the given distance. Use the law of sines to find the angle to steer relative to the direction of the ground vector $\displaystyle 075^\circ$
• Feb 16th 2011, 04:00 PM
Barthayn
Where did you get the 50 degrees from?
• Feb 16th 2011, 04:13 PM
skeeter
Quote:

Originally Posted by Barthayn
Where did you get the 50 degrees from?

basic geometry ...
• Feb 16th 2011, 05:49 PM
Barthayn
I did what you said, and came out with the wrong answer. What did I do wrong? I got an answer of 615.857 km/h. The answer is 598 km/h.

EDIT: Never mind, I redid it and got the correct answer. Must have been a calculation error. Thank you very much. !