# Direction of Resultant Displacement

1. Sep 4, 2014

### mbaha

1. The problem statement, all variables and given/known data

Instructions for finding a buried treasure include the following: Go 572.7 paces at 223◦, turn to 156◦
and walk 124 paces, then travel 417 paces at 242◦

I have already found the magnitude...1015.66 paces
Now I need to find the resultant displacement...

What is the direction of the resultant displacement in degrees? Use counterclockwise from due East as the positive angular direction, between the limits of −180◦ and +180◦

2. Relevant equations
To find magnitude: x=572.7cos(223)+124cos(156)+417cos(242)
x=-418.846-113.28-195.77=-727.896

y=572.7sin223+124sin156+417sin242
y=-390.58+50.4553-368.189=-708.334

-727.896^2+-708.334^2 = sqrt of 529833+501737 = 1015.66 paces

3. The attempt at a solution

To find the direction of the resultant in degrees do I use arctan -708.334/-727.896x
or x1+x2 and y2-y1?

2. Sep 4, 2014

### andrevdh

The arctan will give the required angle. I am not sure at all why you want to use only the x and y components of the first two vectors and not include the third vector since you need to determine the direction of the resultant which would be influenced by the third vector.