Answer
$a). (4)\, south\, of\, west,$
$b). 707m.$
Work Step by Step
a). Since we first go 1000 m N, 500 m W, 1500 m S,
In N-S direction, the stadium is 1500-1000=500 m S to home.
So, the stadium is 500 m W and 500 m S of home. i.e. south of west.
b). Distance = $500\sqrt 2$ = 707m.