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 \(....\,{m}.\)

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Answer & Solution

Correct Answer

(A) \(15\)

Detailed explanation

\(\overrightarrow{{V}}_{{BW}}=4 \sqrt{2} \cos 45 \hat{{i}}+4 \sqrt{2} \sin 45 \hat{{j}}\)

\(=4 \hat{{i}}+4 \hat{{j}}\)

\(\overrightarrow{{V}}_{{w}}=-\hat{{j}}\)

\(\overrightarrow{{V}}_{{B}}=\overrightarrow{{V}}_{{Bw}}+\overrightarrow{{V}}_{{T}}=4 \hat{{i}}+3 \hat{{j}}\)

\(\overrightarrow{{S}}_{{B}}=\overrightarrow{{V}}_{{B}} \times {t}=(4 \hat{{i}}+3 \hat{{j}}) \times 3=12 \hat{{i}}+9 \hat{{j}}\)

\(\left|\overrightarrow{{S}}_{{B}}\right|=\sqrt{(12)^{2}+(9)^{2}}=15\, {m}\)

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