Question

# An airplane flies $400m$ north and $300m$ south and then flies $1200m$ upwards then net displacement is:

A

$1400m$

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B

$1204.15m$

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C

$1300m$

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D

$1500.15m$

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Solution

## The correct option is B $1204.15m$Step 1: GivenDistance travelled in North: ${D}_{1}=400m$Distance travelled in the South: ${D}_{2}=300m$Distance travelled Upwards: ${D}_{3}=1200m$The motion of the plane could be better understood by the following diagram:Step 2: Formula Used$hypotenus{e}^{2}=perpendicula{r}^{2}+bas{e}^{2}$Step 3: Calculate the displacement of the planeCalculate the distance from point A to point C by subtracting the distance of CB from AB$AC=AB-CB\phantom{\rule{0ex}{0ex}}={D}_{1}-{D}_{2}\phantom{\rule{0ex}{0ex}}=400m-300m\phantom{\rule{0ex}{0ex}}=100m$Calculate the distance from point A to point D using the hypotenuse theorem$A{D}^{2}=A{C}^{2}+C{D}^{2}\phantom{\rule{0ex}{0ex}}⇒AD=\sqrt{A{C}^{2}+C{D}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{{100}^{2}+{1200}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{145000}\phantom{\rule{0ex}{0ex}}=1204.15$Hence, the net displacement is $1204.15m$.Thus, option (B) is correct.

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