Answer to Question #240747 in Physics for Butt

Question

Three players on a reality TV show are brought to the center of a large, flat field. Each is given a meter stick, 

a compass, a calculator, a shovel, and (in a different order for each contestant) the following three displacements:

A = 72.4m, 32.0° east of north, B = 57.3m, 36.0° south of west, C = 17.8m due south,

The three displacements lead to the point in the field where the keys to a new Porsche are buried. Two players 

start measuring immediately, but the winner first calculates where to go. What does she calculate?

Answer 1

We do not know, but most likely, to save time and get rid of inconvenient measuring of the magnetic bearing for the three directions, she found the resultant vector of displacement where she needs to go:

$$\vec R=\vec A+\vec B+\vec C,\\\space\\ R_N=72.4\cos32°-57.3\sin36°-17.8=9.92\text{ m},\\ R_E=72.4\sin32°-57.3\cos36°+0=15\text{ m},\\ R=\sqrt{R_N^2+R_E^2}=18\text{ m},\\ \theta=\arctan\frac{R_E}{R_N}=56.5°\text{ E of N.}$$

Thus, instead of rushing to and fro, she most likely walked 18 m at 56.5° in the direction East of North.