A boat leaves a jetty taken as the origin

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

Problem

A boat leaves a jetty taken as the origin O(0,0)O(0,0). It sails 70 m70\,\text{m} east to point PP, then 40 m40\,\text{m} north to point QQ, afterwards 30 m30\,\text{m} west to point RR, and finally 100 m100\,\text{m} north to point SS. Treat the surface of the lake as an xyxy-plane with the usual orientation (east +x+x, north +y+y). (i) Calculate the total path length covered from OO to SS. (ii) Determine the coordinates of point SS. (iii) Find the magnitude and direction of the displacement vector from OO to SS. (iv) Show that the numerical value obtained in part (iii) is smaller than that in part (i). State what this comparison indicates about the efficiency of the route taken.

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