Question

Find the recoil velocity of the gun having mass equal to 5kg. If a bullet of 25g acquires the velocity of 500 m/s after firing of the gun.

Answer 1

momentum is coserved as it is an isolated sys
so 0.025 (500) = 5v
v = 2.5 m/s

Answer 2

$\bf{\underline{\underline{Answer:}}}$

$\bf{-2.5\:m\:s^{-1}}$

$\bf{\underline {Given:}}$

➟ Mass of bullet, $m_1 = 25\:gm=0.025\:kg$

➟ Velocity of bullet before firing, $u_1=0$

➟ Velocity of bullet after firing, $v_1 = 500\:m\:s^{-1}$

➟ Mass of gun, $m_2 = 5\:kg$

➟ Velocity of gun before firing, $u_2 = 0$

$\bf{\underline {To\:Find:}}$

➟ Velocity of gun after firing = ?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

We know that,

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Substituting the values, we get

$0.025×0+5×0=0.025×500+5×v_2$

$⟹ 0 = 12.5 + 5×v_2$

$\:⟹v_2=\dfrac{-12.5}{5}=\bf-2.5\:m\:s{-1}$

Thus, the recoil velocity of gun is equal to $\bf{-2.5\:m\:s^{-1}}$. Here negative (-ve) sign shows that the gun moves in the direction opposite to that of the bullet.