Question

While following the directions on a treasure map a pirate walks 37.0 m north and then turns and walks 8.5 m east what is the magnitude of his resultant displacement?

Answer 1

Answer: $38\ m$

Explanation:

For this exercise you can use the Pythagorean theorem to find the magnitude of the resultant displacement.

Then:

$d^2=\triangle x^2+\triangle y^2$

You can observe that the square of the displacement is equal to the sum of the square  of the horizontal displacement and the square of the vertical displacement.

Since the pirate walks 37.0 meters north and then turns and walks 8.5 meters east:

$\triangle x=37.0\ m\\\triangle y=8.5\ m$

Substituting values and solving for "d", you get:

$d=\sqrt{(37.0\ m)^2+(8.5\ m)^2}\\\\d=38\ m$