Answer to Question #93373 in Classical Mechanics for Akchunya

Question #93373
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
1
Expert's answer
2019-08-27T09:36:00-0400

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

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

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

So, the resultant vector will have coordinates:


x=xA+xB=1.73x=x_A+x_B=1.73y=yA+yB=1y=y_A+y_B=1

The length of the vector:


L=x2+y2=2L=\sqrt{x^2+y^2}=2

Direction:


φ=tan1yx=30\varphi=tan^{-1}{\frac{y}{x}}=30^{\circ}

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


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