An aeroplane if flying with the velocity of $V_{1} = 800$ kmph relative to the air towards south. A wind with velocity of $V_{2} = 15 {ms}^{- 1}$ is blowing from West to East. What is the velocity of the aeroplane with respect to the earth ?

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$150 {ms}^{- 1}$

$40 {ms}^{- 1}$

$222 .7 {ms}^{- 1}$

$82 {ms}^{- 1}$

answer is A.

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Detailed Solution

$V_{1} = 800 \times \frac{5}{18} = \frac{2000}{9} = 222 .2 m / s$
(in south $\bar{V_{1}}$ is –ve)
$∴ \bar{V_{1}} = - 222 .2 \hat{j}; \bar{V_{2}} = 15 \hat{i}$
$|\bar{V_{12}}| = \sqrt{{(222 .2)}^{2} + {(15)}^{2}} = 222 .7 {ms}^{- 1}$

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