Problem 3-25b - Vector difference - Part 4

Determine the vector that must be added to the sum of A and B in the figure to give a net displacement of 4.0kmW.

diagram indicating directions north and east as well as vectors A and B


Accumulated Solution

diagram indicating C at the desired 4 km West

Solution Ax Bx Cx Rx
(A) 5.1cos71 6.8sin52 Cx 4

 

Solution Ay By Cy Ry
(B) 5.1sin71 6.8cos52 Cy 0

5.1cos71+6.8sin52+Cx=45.1sin71+6.8cos52+Cy=0


You should get:
Cx=11kmCy=0.63km

The vector C has a length:

(A)    11+0.63=10.4km

(B)    [(11)2+(0.63)2]1/2=11km

(C)    [(11)2+(0.63)2]=122km