the kinetic energy of a man is half that of boy whose mass is half that of man. when man speeds up by 5m/s his kinetic energy is 100%more than that of boy. the initial velocity of the man is
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Let mass and spend of man be M and v respectively.
Let speed of the boy be v, them
\dfrac {1}{2} Mv^2 = \dfrac{1}{2} \begin{bmatrix} \dfrac{1}{2} \left( \dfrac{M}{2} \right) v^2 \end{bmatrix}
2
1
Mv
2
=
2
1
[
2
1
(
2
M
)v
2
] ...(i)
\dfrac{1}{2} M (v+1)^2 = \dfrac{1}{2} \begin{bmatrix} \dfrac{M}{2} \end{bmatrix} v^2
2
1
M(v+1)
2
=
2
1
[
2
M
]v
2
...(ii)
Dividing Eq. (i) by (ii) we obtain
or \dfrac {v^2} {(v+1)^2} = \dfrac {1}{2}
(v+1)
2
v
2
=
2
1
or \dfrac {v^2} {v+1} = \dfrac {1}{\sqrt2}
v+1
v
2
=
2
1
or \sqrt2 v = v + 1
2
v=v+1
or v ( \sqrt2 - 1) = v+1 v(
2
−1)=v+1
or v = \dfrac {1}{\sqrt2 - 1} m/s v=
2
−1
1
m/s
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