Physics

Problem

A hiker begins her trek from the point

(-10\,\text{m},\,15\,\text{m})

on a map grid. She follows the itinerary below without pausing in between: 1. Walks

25\,\text{m}

60^{\circ}

above the positive

x

–axis. 2. Continues

40\,\text{m}

150^{\circ}

from the positive

x

–axis. 3. Finally moves

30\,\text{m}

at an angle of

-30^{\circ}

(below the positive

x

–axis). a. (i) For each of the three legs, calculate the

x

– and

y

–components. b. (ii) Determine the hiker’s final coordinates on the map. c. (iii) Compute the total path length covered and the magnitude of the net displacement. Verify numerically that the magnitude of the net displacement is less than the total distance walked. d. (iv) Find the angle that the resultant displacement makes with the positive

x

–axis.

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