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gambleongambler · Oct 10, 2009, 07:23 PM

An airplane travels due east for 1.5 hours at 400mph. Then it changes course to S 56 degrees East. Find the airplanes distnace from its point of departure and its bearing after a total fligt time of 4.5 hours.

galactus · Oct 11, 2009, 04:28 AM

If the plane has flown 4.5 hours, then it has traveled 1800 miles.

Draw a picture, label everything, and use the law of cosines.

Let c be the distance back to the point of departure (origin).

$c=\sqrt{600^{2}+1800^{2}-2(600)(1800)cos(146)}$

See why?

gambleongambler · Oct 11, 2009, 06:14 AM

Originally Posted by galactus

If the plane has flown 4.5 hours, then it has traveled 1800 miles.

Draw a picture, label everything, and use the law of cosines.

Let c be the distance back to the point of departure (origin).

$c=\sqrt{600^{2}+1800^{2}-2(600)(1800)cos(146)}$

See why?.

I understand that. But really when the plane was flying southeast, it only flew for 3 hours, because the question asked after a TOTAL flight time of 4.5 hours, and the plane already flew for 1.5 hours. So it flew 1200miles southeast.

But how do I find its bearing to the point of departure?

galactus · Oct 11, 2009, 06:19 AM

OK. Sorry about that. I misread. Just adjust the formula accordingly. Same principle.