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Q. A body goes $20\, km$ north and then $10 \,km$ due east. The displacement of body from Us starting point is:

AFMCAFMC 2003

Solution:

Body goes $20 \,km$ due north along $\overrightarrow{ OA }$ and then $10\, km$ due east along $\overrightarrow{ AB }$
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Net displacement $=\sqrt{(O A)^{2}+(A B)^{2}}$
$=\sqrt{(20)^{2}+(10)^{2}}$
$=\sqrt{400+100}$
$=10 \sqrt{5} km =22.36 \,km$