SOLUTION: A person starts walking from home and walks: 6 miles East 3 miles Southeast 4 miles South 3 miles Southwest 2 miles East This person has walked a total of Find the tota

Algebra ->  Length-and-distance -> SOLUTION: A person starts walking from home and walks: 6 miles East 3 miles Southeast 4 miles South 3 miles Southwest 2 miles East This person has walked a total of Find the tota      Log On


   

Question 1131485: A person starts walking from home and walks:
6 miles East
3 miles Southeast
4 miles South
3 miles Southwest
2 miles East
This person has walked a total of
Find the total displacement vector for this walk:

If this person walked straight home, they'd have to walk miles
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Using vectors with i = 1 mile east ("x positive") and j = 1 mile north ("y positive"),

6 miles E = <6,0>
3 miles SE = <1.5sqrt(2),-1.5sqrt(2)>
4 miles S = <0,-4>
3 miles SW = <-1.5sqrt(2),-1.5sqrt(2)>
2 miles E = <2,0>

The total distance the person has walked is 6+3+4+3+2 = 19 miles

The total displacement vector is the sum of all the vectors: <8,-4-3sqrt(2)>

The distance the person must walk to walk straight home is the magnitude of the vector: sqrt%288%5E2%2B%284%2B3sqrt%282%29%29%5E2%29 = sqrt%2864%2B16%2B24sqrt%282%29%2B18%29 = sqrt%2898%2B24%2Asqrt%282%29%29 = 11.487 miles approximately