Answer to Question #280147 in Classical Mechanics for Valya

Question

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.

Answer 1

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

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

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

All angles are from positive x-axis.