Homework: Vectors (Section 8.4)

Question

A person leaves home and walks 3 miles west, then 5 miles southwest.

How far from home is she?

   miles=

In what direction must she walk to head directly home?

   degrees North of East=

Answer 1

miles from home = about 6.49

distance squared = (5sqr2/2)^2 + (3+5sqr2/2)^2 = 34+5sqr2

distance = square root of (34+5square root of 2) = 6.49 miles

she needs to go back at 44.6 degrees North of East

the angle whose sine = 5sqr2/2 over 3+5sqr2/2=7.07/10.07

sin^-1(.702) = 44.6 degrees, slightly more easterly than NE