A) \[\sqrt{2}m/s\]
B) \[(\sqrt{2}-1)m/s\]
C) \[\frac{1}{\sqrt{2}}m/s\]
D) \[\frac{1}{\sqrt{2}-1}m/s\]
Correct Answer: D
Solution :
Let mass and speed of man be\[M\]and\[v\] respectively. Let speed of the boy be\[v,\]then \[\frac{1}{2}M{{v}^{2}}=\frac{1}{2}\left[ \frac{1}{2}\left( \frac{M}{2} \right){{v}^{2}} \right]\] ...(i) \[\frac{1}{2}M{{(v+1)}^{2}}=\frac{1}{2}\left[ \frac{M}{2} \right]{{v}^{2}}\] ...(ii) Dividing Eq.. (i) by (ii) we obtain \[\frac{{{v}^{2}}}{{{(v+1)}^{2}}}=\frac{1}{2}\] Or \[\frac{v}{v+1}=\frac{1}{\sqrt{2}}\] Or \[\sqrt{2}v=v+1\] Or \[v(\sqrt{2}-1)=1\] Or \[v=\frac{1}{\sqrt{2}-1}m/s\]
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