A butterfly is flying with a velocity <math> <mrow> <mn>4</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> 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:

v → B W = 4 2 ( c o s 4 5 ° i ^ + s i n 4 5 ° j ^ ) = 4 i ^ + 4 j ^ , a n d v → W g = 0 i ^ − j ^  v → B g = v → B W + v → W g = ( 4 i ^ + 4 j ^ ) + ( 0 i ^ − j ^ ) = 4 i ^ + 3 j ^ | v → B g | = 5 m / s ⇒ S p e e d o f B u t t e r f l y Magnitude of displacement of Butterfly =  | v → B g | × t = 5 × 3 = 1 5 m

A butterfly is flying with a velocity <math> <mrow> <mn>4</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> 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:

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Physics Class 11th Physics Motion in Plane

A butterfly is flying with a velocity $4 \sqrt[]{2} m / s$ 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:

Option 1 -

15m

Option 2 -

20m

Option 3 -

Option 4 -

$12 \sqrt[]{2} m$

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

${\vec{v}}_{B W} = 4 \sqrt[]{2} (c o s 45 ° \hat{i} + s i n 45 ° \hat{j}) = 4 \hat{i} + 4 \hat{j}, a n d {\vec{v}}_{W g} = 0 \hat{i} - \hat{j}$

${\vec{v}}_{B g} = {\vec{v}}_{B W} + {\vec{v}}_{W g} = (4 \hat{i} + 4 \hat{j}) + (0 \hat{i} - \hat{j}) = 4 \hat{i} + 3 \hat{j}$

$| {\vec{v}}_{B g} | = 5 m / s \Rightarrow S p e e d o f B u t t e r f l y$

Magnitude of displacement of Butterfly = $| {\vec{v}}_{B g} | \times t = 5 \times 3 = 15 m$

<math> <mrow> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>B</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>4</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mrow> <mo>(</mo> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>4</mn> <mn>5</mn> <mo>°</mo> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>4</mn> <mn>5</mn> <mo>°</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>4</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>,</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>W</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>−</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>               <math> <mrow> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>B</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>B</mi> <mi>W</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>W</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>4</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>4</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>−</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>3</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>       <math> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>B</mi> <mi>g</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>5</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mo>⇒</mo> <mi>S</mi> <mi>p</mi> <mi>e</mi> <mi>e</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <mi>o</mi> <mi>f</mi> <mtext> </mtext> <mtext> </mtext> <mi>B</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mi>f</mi> <mi>l</mi> <mi>y</mi> </mrow> </math> Magnitude of displacement of Butterfly =  <math> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>B</mi> <mi>g</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mo>×</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> <mo>×</mo> <mn>3</mn> <mo>=</mo> <mn>1</mn> <mn>5</mn> <mi>m</mi> </mrow> </math>

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A butterfly is flying with a velocity $4 \sqrt[]{2} m / s$ 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:

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A butterfly is flying with a velocity 4 2 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:

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A butterfly is flying with a velocity $4 \sqrt[]{2} m / s$ 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: