The kinetic energy of a person is just half of kinetic energy of a boy whose mass is just half of that person. If person increases his speed by 1 m/s then his-kinetic energy becomes equal to that of boy. Initial speed of person was

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$(2 + \sqrt{2}) m / s$

$(\sqrt{2} + 1) m / s$

$2 (\sqrt{2} + 2) m / s$

none of these

answer is A.

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Detailed Solution

Let initial speed of man of mass m be u then
$K_{man} = \frac{1}{2} {mu}^{2} and K_{boy} = 2 \times \frac{1}{2} {mu}^{2} = {mu}^{2}$
Now if man increases his speed by 1 m/s then
$\begin{array}{l} K_{man}^{'} = K_{boy} \Rightarrow \frac{1}{2} m (u + 1)^{2} = {mu}^{2} \\ \Rightarrow \frac{u + 1}{u} = \sqrt{2} \Rightarrow u = \frac{1}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} = (\sqrt{2} + 1) m / s \end{array}$