Question

An explorer hikes 4 miles due east, 7 miles due south, then 3 miles due east, then 1 mile due north, and finally then 2 miles due west. How far is he from his original position?

Answer 1

7.81 miles

Explanation:

Assume Eastern and Southern displacement as positive and Northern and Western displacement as negative, the explorer's East-West and South-North displacements were:

`E=4+3-2=5\ miles\\S=7-1=6\ miles`

His distance from his original position is:

`D^2 = E^2+S^2\\D=√(5^2+6^2)\\ D= 7.81\ miles`