In an explosion, a piece of debris is tossed 99 meters N 45 W. what is the displacement in the north and west directions. I'm not really sure what it wants when it asks for displacement so I also don't know how to get it.

Answer 1

N45W ---> an angle of 135° using trig notation.

So we are de-composing your vector into its vertical and horizontal displacement.
horizontal: 99cos 135
= 99(-√2/2) = appr - 70 metres
vertical : 99 sin 135° = appr 70 metres

notice if you construct a right-angled triangle in the 2nd quadrant having an angle of 135° and a hypotenuse of 99 metres, the height can be found:
h/99 = sin135 ----> h = 99sin135 = appr 70
the base is :
b/99 = cos135 ----> b = 99cos 135 = appr -70
the ordered pair of the end of the hypotenuse is about (-70, 70)