Answer to Question #225359 in Physics for Gelo

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

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