Question #280147

Find the magnitude and direction of the vector represented by the following pairs of components:

(a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m., Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.


1
Expert's answer
2021-12-16T11:33:33-0500

(a) A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=149°.A=\sqrt{A_x^2+A_y^2}=10\text{ cm},\theta=\arctan(A_x/A_y)=149°.

(b) A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=194°.A=\sqrt{A_x^2+A_y^2}=10\text{ cm},\theta=\arctan(A_x/A_y)=194°.

(c) A=Ax2+Ay2=8.2 cm,θ=arctan(Ay/Ax)=19°.A=\sqrt{A_x^2+A_y^2}=8.2\text{ cm},\theta=\arctan(A_y/A_x)=-19°.

All angles are from positive x-axis.


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