Adding Vectors (Physics)?

Question

I was able to complete all of the other problems, but this one is much more difficult and I am completely lost..

A squirrel is wandering around a yard. It hops 2.2m at an angle of 74 degrees north of east. Then it scurries 3.1m at an angle of 85 degrees north of west. Finally, it runs 1.7m at an angle of 15 degrees south of west. What are the magnitude and direction for the squirrel's total displacement?

If anyone can help me I'd greatly appreciate it..Thanks!!

Answer 1

East - West:
2.2cos74 - 3.1cos85 - 1.7cos15 = -1.30585m
North - South:
2.2sin74 + 3.1sin85 - 1.7sin15 = 4.76299m
Magnitude:
MAG = √[(1.30585)^2 + (4.76299)^2] = 4.93876m
Direction:
DIR = arc tan(4.76299/1.30585) = 74.6682 degrees north of west

Answer 2

One tricky part is to convert each vector from (r, t) form to (x, y) form using...
x = r * cos t
y = r * sin t

The other twist they tossed in giving the angles in terms of D degrees M of N.

D north of east = D
D north of west = 180 - D
D south of west = 180 + D

So...
r1 = 2.2m, t1 = 74 degrees
r2 = 3.1m, t2 = 95 degrees
r3 = 1.7m, t3 = 195 degrees

Find x1, y1, x2, y2, x3, y3. Add all the x values to get xtotal and all the y values to get ytotal.

Then rtotal = sqrt(xtotal^2 + ytotal^2)
ttotal = arctan(ytotal/xtotal)

BUT... add 180 degrees to ttotal if ytotal<0

Answer 3

v1 = 2.2*(cos74 i + sin74 j)
v2 = 3.1*(cos105 i + sin105 j)
v3 = 1.7*(cos195 i + sin195 j)

v = v1 + v2 + v3

then find |v| and the direction is given by the unit vector

n = v/|v| whose components should be

n = cos(theta) i + sin(theta) j = ni * i + nj * j
so you can figure out theta, but you won't know the sign. Take

if y>=0
theta = acos(ni)
else y<0
theta = -acos(ni) or 360 - acos(ni)

will get you the right sign because acos is only defined over theta=[0 to 180]. Im doing all my angles in degrees but you can convert it to radians if you want.

Answer 4

Choose a coordinate system.
Convert all those angles into your coordinate system.
Find the x and y components of each vector using sin and cos.
Add x components to get the resultant x component.
Add y components to get the resultant y component.

use tangent and the pythagorean theorem to convert your answer into direction and magnitude.