Plane direction after wind?

anshu

An airplane pilot flies a plane that has an air speed of 450 mi/H. She needs to fly from Denver to Chicago, which lies on a line 1150 miles long at an angle of 25 degrees north of east (measured from Denver.) A constant jet stream of 280 mi/H is coming from the southeast (ie, along the 45 degree line between south and east.) Determine the compass heading that she must use in order to get to Chicago in a straight line, and determine the flight time needed to make the trip.

me and my friends have tried just about everything we know, we tried to assume that the final speed was 450 but that idea was shot down. I really am clueless some help would be much appriciated
thanks in advance

Hypercase

Hi Anshu. Drawing a diagram, the situation ends up looking like this:-
Wind(velocity vector):- 280cos 45 i + 280 sin45 j
Plane (velocity vector):- 450 cos x i + 450 sin x j
Path to be taken(displacement vector):- 1150 miles & 25 degrees north of east
so we hav total knowledge of the wind vector, but only know the size of the Plane(direction not known) and we know the resultant direction needed, but do not know the resultant speed.
applying sine rule twice we get that the direction of travel which is 10.78 degrees south of west. (while writing as components x = 190.78)
using that in :-
(450 cos x i + 450 sin x j) + (280cos 45 i + 280 sin45 j) = R cos 155 i + R sin 155 j

direction of travel of the plane is 10.78 degrees south of west.
we get R(resultant velocity) = 269.31 mi/h
therefore, time taken = 4 hours 16 minutes 12 seconds.

Hey a diagram would make this situation seem a lot simpler.
If u would like to see the diagram i used, Plz answer the following:-
How the hell do i load a attachment?
Ive tried drawing it in paint, but the file size comes otu too large

anshu

thanks, didnt know the law of sines, but being able to check answers was helpful thanks again