First slide

Motion in a plane

Question

A car makes a displacement of 100 m towards east and then 200 m towards north. Find the magnitude and direction of the resultant displacement.

Moderate

Solution

$\large \overrightarrow {{d_1}} = 100\widehat i\;m$
$\large \overrightarrow {{d_2}} = 200\widehat j\;m$
$\large \therefore \overrightarrow d = \overrightarrow {{d_1}} + \overrightarrow {{d_2}} = (100\widehat i + 200\widehat j)\;m$
$\large \therefore \overrightarrow {|d} | = \sqrt {{{100}^2} + {{200}^2}} \;m = 223.6\;m\$
Direction $\large \theta = {\tan ^{ - 1}}\frac{{200}}{{100}} = {\tan ^{ - 1}}(2)\$ , north of east

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