Problem 3-25b - Vector difference - Part 5 - (C)

Determine the vector that must be added to the sum of $A$ and $B$ in the figure to give a net displacement of $4.0\; km\; \text{W}$ .

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	$A_x$	$B_x$	$C_x$	$R_x$
(A)	5.1 cos 71	6.8 sin 52	$C_x$	-4

Solution	$A_y$	$B_y$	$C_y$	Ry
(B)	$-5.1 \sin 71$	$6.8 \cos 52$	$C_y$	$0$

$5.1 \cos71 + 6.8 \sin52 + C_x = -4 \\ -5.1 \sin71 + 6.8 \cos52 + C_y = 0$

$C_x = -11 \;km \\ C_y = 0.63 \;km$

$|C| = 11 \;km$

Correct

$\theta = tan^{-1}C_y/C_x = tan^{-1} \;0.63/11 = 3.3^\circ$

In which direction is this?

(A) north of west

(B) south of west

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