A person starts walking from home and walks:

Question

4 miles East

5 miles Southeast

6 miles South

2 miles Southwest

4 miles East

This person has walked a total of _______ miles

Find the total displacement vector for this walk: _______

If this person walked straight home, they'd have to walk _______ miles

Answer 1

Total distance walked is the sum of 21 miles.

Split into components: On the diagonals Southeast and Southwest, each leg is hypotenuse * √(2) /2.

So x = sum [+4 +5√(2) /2 +0 - √2 +4] = 10.13 mi.

and y = sum [ 0 -5√(2) /2 -6 -√2 +0] = -10.95 mi. Vector = <10.13, -10.95>.

Pythagorean Theorem gives straight line distance = displacement = 14.92 miles.