A butterfly is flying with a velocity $4 \sqrt{2} \mathrm{~m} / \mathrm{s}$ in North-East direction. Wind is slowly blowing at $1 \mathrm{~m} / \mathrm{s}$ from North to South. The resultant displacement of the butterfly in 3 seconds is :

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Kinematics

A butterfly is flying with a velocity

42 m / s

in North-East direction. Wind is slowly blowing at

1 m / s

from North to South. The resultant displacement of the butterfly in 3 seconds is :

(A)15 m✓ Correct
(B)20 m
(C)3 m
(D) $122 m$

Answer: (A)

Solution

Take

\hat{i}

towards the east and

\hat{j}

towards the north. The butterfly's own velocity is

42 (cos 4 5^{\circ} \hat{i} + sin 4 5^{\circ} \hat{j}) = 4 \hat{i} + 4 \hat{j}

m/s, and the wind, blowing from north to south, adds

- 1 \hat{j}

m/s. The resultant velocity is

v = 4 \hat{i} + 3 \hat{j} m/s, ∣ v ∣ = 16 + 9 = 5 m/s

The velocity is constant, so in

3

s the displacement has magnitude

5 \times 3 = 15

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option

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