PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Three arbitrary vectors A(A,α), B(B,β) and C(C,γ) act in the same plane, where the bracketed symbols denote magnitude and the angle each vector makes with the positive x–axis. Answer the following:
(i) Write the expressions for the rectangular components Ax,Ay, Bx,By and Cx,Cy in terms of the given magnitudes and angles.
(ii) Hence obtain expressions for the rectangular components Rx and Ry of the resultant vector R=A+B+C.
(iii) Using the results of part (ii), derive general formulae for the magnitude R and the direction θ of R with respect to the positive x–axis.
(iv) Explain why the relations obtained in parts (ii) and (iii) remain valid for the sum of any number of coplanar vectors expressed in rectangular components.