A person starts from the origin of a Cartesian coordinate system and follows the path…

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

Problem

A person starts from the origin

O

of a Cartesian coordinate system and follows the path described below on level ground. (i) She walks

200\,\text{m}

due east to point

A

. (ii) From

A

she walks

150\,\text{m}

at an angle

30^{\circ}

north of east to reach point

B

. (iii) Finally, from

B

she walks

100\,\text{m}

due south to reach point

C

. Taking

+x

east and

+y

north, calculate the x and y components of each leg of the journey and hence find the x and y components of the displacement vector

\overrightarrow{OC}

. Then determine the magnitude and direction of

\overrightarrow{OC}

with respect to the positive x-axis.