Question

A delivery truck travels 22 blocks north, 16 blocks east and 26 blocks south. What is its final displacement from the origin? Assume the blocks are equal length.
Magnitude
16.5 blocks
Direction
-166.0 ° (counterclockwise from east is positive)

-magnitude is correct but direction is not. Other incorrect guesses for direction include: +166, +/- 147.

Answer 1

Vertical displacement:

22 blocks north + 26 blocks south
north will be negative, south positive
so:
-22 block + 26 blocks = 4 blocks

(4 blocks to the south)

horizontal displacement:
16 blocks east

So, we use trigonometry to calculate the angle.
Angle x will be the angle made between the hypotenuse (the final displacement) and the horizontal displacement.

So Tan x = (4/16)
So x = tan^-1 (4/16)
So x =14.04º aprox

then to calculate the magnitude of the hypotenuse we just use Pythagoras' theorem.

so:
16^2 + 4^2 = D^2
256 + 16 = D^2
272 = D^2
D= 16.5 aprox.

You said something that counterclockwise is positive. So, it moved in 360º - 14.04º = 345.96º

So, in summary:
It moved 16.5 blocks in 345.96º from East