First slide

Vectors

Question

Consider east as positive x-axis, north as positive y-axis. A girl walks 10 m east first time then 10 m in a direction $30^{0}$ west of north for the second time and then third time in unknown direction and magnitude so as to return to her initial position. What is her third displacement in unit vector notation?

Moderate

A

$- 5 \hat{i} - 5 \sqrt{3} \hat{j}$
B

$5 \hat{i} - 5 \sqrt{3} \hat{j}$
C

$- 5 \hat{i} + 5 \sqrt{3} \hat{j}$
D

She cannot return

Solution

$\vec{s_{1}} + \vec{s_{2}} + \vec{s_{3}} = 0$
$10 \hat{i} + [10 \sin 30 (- \hat{i}) + 10 \cos 30 \hat{j}] + \vec{s_{3}} = 0$
$(10 - 5) \hat{i} + 5 \sqrt{3} \hat{j} + \vec{s_{3}} = 0$
$\vec{s_{3}} = - 5 \hat{i} - 5 \sqrt{3} \hat{j}$

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