A particle starts from the origin and undergoes three successive displacements

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A particle starts from the origin and undergoes three successive displacements, each of magnitude 10 m10\,\text{m}, making angles 0∘0^{\circ}, 120∘120^{\circ} and 240∘240^{\circ} respectively with the positive xx–axis. (i) Determine the xx– and yy–components of each displacement. (ii) Show that the particle returns to its starting point after the three displacements. (iii) Generalise this result by proving that nn equal‐magnitude displacement vectors whose directions are equally spaced by an angle 360∘n\frac{360^{\circ}}{n} in the plane add up to give a zero resultant.

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