Question

When a man increases his speed by $2\, ms^{-1}$, the finds that his kinetic energy is doubled, the original speed of the man is

• A. $2(\sqrt{2}-1)ms^{-1}$
• B. $2(\sqrt{2}+1)ms^{-1}$
• C. $4.5\,ms^{-1}$
• D. None of these

Answer 1

Answer: (B)

$2(\sqrt{2}+1)ms^{-1}$

Answer 2

Man possesses kinetic energy, because of its velocity $(v)$.
When in is mass of man, then
$K=\frac{1}{2} m v^{2}$
Given $v_{1}=v, m_{1}=m_{2}=m, v_{2}=(v+2) m s^{-1}$
$K_{2}=2 K_{1}$
$\therefore \frac{K_{1}}{K_{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}$
$\frac{K_{1}}{2 K_{1}}=\frac{v^{2}}{(v+2)^{2}}$
$\Rightarrow v^{2}-4 v-4=0$
$\Rightarrow v_{1}=\frac{4+\sqrt{16+16}}{2}$
$=\frac{4+\sqrt{32}}{2}$
$=2(2 \sqrt{2}+1) m s^{-1}$