Question

The muzzle velocity of a 50.0g shell leaving a 3.00 kg rifle is 400m/s what is the recoil velocity of the rifle

Answer 1

Here if we consider bullet and gun as a system then we can say that momentum of the system will remain conserved

so we will have

$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$

now we know that

$m_1 = 50 g = 0.050 kg$

$m_2 = 3 kg$

$v_{1i} = v_{2i} = 0$

$v_{1f} = 400 m/s$

now we will have

$0.050(0) + 3(0) = 0.050(400) + 3(v)$

$20 + 3v = 0$

$v = - \frac{20}{3} = - 6.67 m/s$

so gun will recoil with speed 6.67 m/s