A courier van follows the route described below

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A courier van follows the route described below, starting from a warehouse at point

W

. Leg 1: Drives

6\text{ km}

due east in

8\text{ min}

. Leg 2: Drives

4\text{ km}

due north in

6\text{ min}

. Leg 3: Drives

5\text{ km}

on a bearing of

210^{\circ}

7\text{ min}

. Leg 4: Drives

3\text{ km}

due west in

4\text{ min}

. Respond to the following: (i) Express each leg as a displacement vector in the form

x\hat{i}+y\hat{j}

with units in kilometres. (ii) Calculate the resultant displacement vector from point

W

after completing the four legs, and find its magnitude and bearing (clockwise from north). (iii) Determine the total time taken for the journey and hence compute the average velocity vector of the van (in km min

^{-1}

) together with its magnitude and direction. (iv) If the van travels back to

W

along the straight-line path at the same average speed found in part (iii), find the time required for the return trip, correct to the nearest second.

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