Question

Given the three vectors below, graph and calculate the magnitude and angle of the resultant vector using analytical method. Use an accurate scale for graphing.

A= 7m/s, 0 degree eastward

B= 6m/s, 30 degree north of east

C= 4m/s, 45 degree north of west

Answer 1

Given:

$A_x=7.0,\quad A_y=0$

$B_x=6\cos 30^{\circ}=5.2,\quad B_y=6\sin 30^{\circ}=3.0$

$C_x=-4\cos 45^{\circ}=-2.8,\quad C_y=4\sin 45^{\circ}=2.8$

The resultant vector have compotents

$$D_x=A_x+B_x+C_x=7.0+5.2-2.8=9.4\\ D_y=A_y+B_y+C_y=0+3.0+2.8=5.8$$

The magnitude

$$R=\sqrt{R_x^2+R_y^2}=\sqrt{9.5^2+5.8^2}=11$$

Angle

$$\theta=\tan^{-1}\frac{R_y}{R_x}=\tan^{-1}\frac{5.8}{9.4}=32^{\circ}\quad \rm N\:of\:E$$