A person starts walking from home and walks:

Question

A person starts walking from home and walks:
4 miles East
7 miles Southeast
6 miles South
1 miles Southwest
3 miles East

 

This person has walked a total of -- miles

Find the total displacement vector for this walk: -i + - j

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

 

Answer 1

1. walked for 21 miles

* the displacement is y = 4*sqrt(2) + 6 and x = 7 + 3* sqrt(2)

Let a = 3 - sqrt(2)/2 , b = 4 + 7*sqrt(2)/2 , c = sqrt(2)/2 + y, d = 6 + 7*Sqrt(2)/2

Solve the proportion a/b = c/d for y.

Then

z = sqrt ( (4 + 7*Sqrt(2)/2)^2 + (6 + 7*sqrt(2)/2))^2

k = sqrt( ( y +sqrt(2)/2))^2 + (3 - sqrt(2)/2)^2 )

z+k is straught line

diagram called walk.jpg