I know how to do displacement, I just get confused by the directions. I walk 6 blocks east and 5 blocks north-I come up with 7.8 because I squared 6 + squared 5 and took the square root of 61 but do I say the final displacement is 7.8 blocks east of north or 7.8 blocks north of east-that's where I'm confused.

Question

Thank you

Answer 1

Try it with x and y
x is east and y is north

start at (0,0)
go east 6 to (6,0)
now go north 5 to (6,5)

now what angle north of east is (6,5)?
tan angle = y/x = 5/6 so angle = 39.8 deg
usually you want compass directions clockwise from north though so
90 = 39.8 = 50.2 degrees east of north
now I better check your distance
sqrt(36+25) = sqrt 61 = 7.8 check
so
you went 7.8 blocks at 50.2 degrees east of north