What is the direction of the displacement of a person who walks 10 km at 37 degrees south of east, then 14 km due west?

To determine the direction of the displacement, we can break down the two legs of the journey and find their resultant vector.

First, let's calculate the components of the first leg:

Distance = 10 km
Direction = 37 degrees south of east

To find the east and south components, we use trigonometric functions:

East component = Distance * cos(direction) = 10 km * cos(37°)
South component = Distance * sin(direction) = 10 km * sin(37°)

Next, let's calculate the components of the second leg:

Distance = 14 km
Direction = Due west (opposite to the east direction)

Since we're going due west, the east component will be negative:

East component = -14 km
South component = 0 km (no movement in the north-south direction)

Now, to find the resultant vector, we add the individual components:

Resultant east component = (10 km * cos(37°)) + (-14 km)
Resultant south component = (10 km * sin(37°)) + 0 km

Using these component values, we can calculate the magnitude and direction of the resultant displacement vector using the Pythagorean theorem:

Magnitude = sqrt((Resultant east component)^2 + (Resultant south component)^2)
Direction = arctan(Resultant south component / Resultant east component)

Plug in the values and calculate the direction by converting it into compass bearing if necessary.

(10cos37,-10sin37)+(-14,0) = (-6,-6)