Answer to Question #93373 in Classical Mechanics for Akchunya

Question

Vector A = 6.0 m and points 30° north of east. Vector B = 4.0 m and points 30° south of west. The resultant
vector A + B is given by?
I have tried this Question many times and have not been able to figure it out, Please help me

Answer 1

For this task first, lets find X (East) and Y (North) components of each vector, and then sum them up.

$$x_A=6*\cos30^\circ=5.19$$ $$y_A=6*\sin30^\circ=3$$

$$x_B=-4*\cos30^\circ=-3.46$$ $$y_B=-4*\sin30^\circ=-2$$

So, the resultant vector will have coordinates:

$$x=x_A+x_B=1.73$$ $$y=y_A+y_B=1$$

The length of the vector:

$$L=\sqrt{x^2+y^2}=2$$

Direction:

$$\varphi=tan^{-1}{\frac{y}{x}}=30^{\circ}$$

Answer: resultant vector has the length of 2.0m and points 30 degrees north of east