Q75 / 90 · JEE Main 2021 (20 Jul Shift 1) · Physics

A butterfly is flying with a velocity $4 \sqrt{2} m s^{- 1}$ in north-east direction. Wind is slowly blowing at $1 m s^{- 1}$ from north to south. The resultant displacement of the butterfly in $3$ seconds is:

A
$3 m$
B
$20 m$
C
$12 \sqrt{2} m$
Correct answer
D
$15 m$

Solution

${\vec{V}}_{BW} = 4 \sqrt{2} \cos 4 5 \hat{i} + 4 \sqrt{2} \sin 4 5 \hat{j}$
$= 4 \hat{i} + 4 \hat{j}$
${\vec{V}}_{w} = - \hat{j}$
${\vec{V}}_{B} = {\vec{V}}_{BW} + {\vec{V}}_{w} = 4 \hat{i} + 3 \hat{j}$
${\vec{S}}_{B} = {\vec{V}}_{B} \times t = (4 \hat{i} + 3 \hat{j}) \times 3 = 12 \hat{i} + 9 \hat{j}$
$|{\vec{S}}_{B}| = \sqrt{(12)^{2} + (9)^{2}} = 15 m$

Hence, the correct answer is option: 'D'.

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A butterfly is flying with a velocity 42 m s-1 in north-east direction. Wind is slowly blowing at 1 m s-1 from north to south. The resultant displacement of the butterfly in 3 seconds is:

Solution

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A butterfly is flying with a velocity $4 \sqrt{2} m s^{- 1}$ in north-east direction. Wind is slowly blowing at $1 m s^{- 1}$ from north to south. The resultant displacement of the butterfly in $3$ seconds is: