Answer:
Here, the
mass of the bullet, \[{{m}_{1}}=0.02kg\]
Mass of gun, \[{{m}_{2}}=75kg\]
Velocity of
bullet, \[{{\upsilon }_{1}}=200m/s\]and the speed of gun, \[{{\upsilon
}_{2}}=?\]
According to
law of conservation of momentum,
Total momentum
of system after firing = Total momentum of system before firing
i.e., \[{{m}_{1}}{{\upsilon
}_{1}}+{{m}_{2}}{{\upsilon }_{2}}=0\]
(Since
initial velocities of gun and bullet before firing is zero.)
or \[0.02\times
200+7.5\times {{\upsilon }_{2}}=0\]
or \[7.5\times
{{\upsilon }_{2}}=-0.02\times 200\]
or \[{{\upsilon
}_{2}}=-\frac{4}{7.5}=-0.533\]
or \[{{\upsilon
}_{2}}=-0.53m/s\]
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