A hiker travels in a straight line for a distance of on a bearing of west of north

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

Problem

A hiker travels in a straight line for a distance of

6.00\,\text{km}

on a bearing of

25^{\circ}

west of north. Use due north as the

+y

axis and due east as the

+x

axis. (a) Calculate the signed

x

and

y

displacements (in kilometres) for the hiker’s trek. (b) Write the displacement vector in unit-vector notation using

\hat{i}

(east) and

\hat{j}

(north). (c) Briefly comment on how the numerical signs of the components relate to the hiker’s compass bearing.