My professor gave me this problem as a homework question, but I can\'t understan

Question

My professor gave me this problem as a homework question, but I can't understand it at all. can you help me?

three successive displacements in a 55 A particle undergoes plane, as follows: di, 4.00 m southwest; then d, 5.00m east and finally ds, 6.00 m in a direction 60.0° north of east. Choose a coor dinate system with the y axis pointing north and thex axis pointing east.What are (a) the x component and (b) the y component of di? What are (c) the x component and (d) the y component of d,? What ae (e) the x component and (f) the y component of d3? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the x component, (h) the y component, (i) the magnitude, and (j) the direction of the net dis- placement? If the particle is to return directly to the starting point, (k) how far and (1) in what direction should it move?

Explanation / Answer

Given:
a = 4 m
b = 5m
c = 6 m

Theta=60 degrees

For vector a we get

A=-acos theta i+(-asin theta)j

Since it is going southwest so the components will be -ve

=-4cos 60 i-4 sin 60 j

=-2i-3.4j

Likewise B vector is going eastward so the bx=b and by =0

B=5i+0j

B=5i

Now C vector will be

C=6cos 60i+6sin 60 j

=3i+5.19j

Resultant R =vector A+vector B

Net displacement

=vector C-(vector A+vector B)

=(3i+5.19j)-(-2i-3.4j+5i)

=3i+5.19j+2i-1.6j

=5i+3.59j

R=undrt(5^2+3.59^2)

=6.15 m

Thetha=arctan(3.59/5)

=35.5 degrees

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