Question

While following the directions on a treasure map, a pirate walks 23.5 m north, then turns and walks 2.7 m east.
What is the magnitude of the single
straight-line displacement that the pirate could have taken to reach the treasure?
Answer in units of m

Answer 1

Here's what you know,
Dy = 23.5 m, and Dx = 2.7m.
Use the formula
d = (Dx^2 + Dy^2)^ (1/2)
d = (23.5^2 + 2.7^2)^((1/2) = 23.65m
d = 24m (significant digits).
Since they have only asked for magnitude, its 24m.
If they ask for direction then,
theta = tan-1( Dy / Dx )
= tan-1( 23.5 / 2.7)
theta = 83.4 deg or 83 deg (significant digits)