what is the magnitude of his displacement?

john walks 1.00 km north, then turns right and walks 1.00 km east.  his speed is 1.50 m/s during the entire stroll.
a) what is the magnitude of his displacement, from beginning to end?
b) if jane starts at the same time and place as john, but walks in a straight line to the endpoint of john's stroll, at what speed should she walk to arrive at the endpoint just when john does?

since north and east are at right angles, john's displacement is the diagonal across a square with a length of 1 km on each side.  by the pythagorean theorem d = √(1^2 + 1^2) = √(1 + 1) = √2 ≈ 1.4142 km.
 
jane needs to walk √2 km in the same time it takes john to walk 2 km, so she need only walk √2/2 as fast.
 
his speed was 1.5 m/s, her speed is only (1.5)(√2)/2 m/s = 1.0607 m/s.