Physics Flight problem?

Question

Uri is on a flight from Boston to Los Angeles. His plane is traveling 25.0 degrees south of west at 300 mph . Val is on a flight from Miami to Seattle. Her plane is traveling 35.0 degrees north of west at 300 mph. Somewhere over Kansas, Uri's plane passes 1000 ft directly over Val's plane. Uri is sitting on the right side and can see Val's plane below him after they pass. Uri notices that the fuselage of Val's plane doesn't point in the direction that her plane is moving.
What is the angle between the fuselage and the direction of motion?

Answer 1

This requires a translation of reference frame. The problem is stated with respect to the Earth as reference frame (compass points). Since Uri is the observer, the reference frame must be his plane as if it is at rest and the relative speeds and directions are computed as follows. Note that I retain the points of the compass w/r/t Uri:

W = Val-300*cos(25)
N=Val+300*sin(25)

W=300*(cos(35)-cos(25))
=-26.15 mph
So Val is receeding from Uri in this direction

N=300*(cos(35)+sin(25))
=298 mph

so the angle of direction of Val w/r/t Val's fuselage direction as observed from Uri's plane is

90-35+Atan(26.15/298)

=60 degrees

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