Question

If a crow flies west for 60 km and then south for 45 km, what is the direction of its displacement?

Answer 1

That's 105 km that he flew, or 65.2 miles !  I'm absolutely positive
that the crow must have landed and gotten some rest when you
weren't looking.  But that had no effect on his displacement when
he got where he was going, so we can continue to solve the problem:


The displacement is the distance and direction from the place
where the crow took off to the place where he landed.

-- It's distance is the hypotenuse of the right triangle whose legs
are 60 km and 45 km.

        D²  =  (60 km)²  +  (45 km)²

              =    3,600 km²  +  2,025 km²  =  5,625 km²

         D  =  √(5625 km²)  =  75 km .    
 
-- It's direction is the angle whose tangent is  (45 S / 60 W).

         tan⁻¹ (45/60)  =  tan⁻¹ (0.75)  =  36.9° south of west

                                                         =  53.1° west of south.

                                                         =  not exactly southwest but close.