Question 1150167: A person starts walking from home and walks:
6 miles East
4 miles Southeast
4 miles South
6 miles Southwest
3 miles East
This person has walked a total of (answer) miles
Find the total displacement vector for this walk:
If this person walked straight home, they'd have to walk (answer) miles
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Do this on a cartesian coordinate system
He goes from the origin to (6, 0) the 45 degrees southeast, which is 4/sqrt(2) or 2 sqrt(2) units positive x and negative y. That is (8 sqrt(2),-2 sqrt(2)) then 4 units south to ( 8 sqrt(2), -6 sqrt(2))
southwest 6 is x negative and y negative 3 sqrt(2) for each to (5 sqrt(2), -9 sqrt (2))
3 east is (8 sqrt(2), -9 sqrt(2))
They walked 23 miles total
they went from (0, 0) to (8 sqrt(2), -9 sqrt(2))
The tangent of theta, the angle from east to south, is 9 sqrt(2)/8 sqrt(2)=9/8
arc tan of that is 48.37 degrees or 138.47 degrees, a little south of SSE.
The straight home distance is the sqrt of those two coordinates squared or
sqrt(128+162)=sqrt(290)=17.03 miles
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