Question

find the recoil velocity of a gun having mass equal to 5kg, if bullet of 25gm acquires the velocity of 500m/s after firing from the gun

Answer 1

momentum before firing

= 5.025× 0 + = 0

Momentum after firing
5 × v + 0.025 × 500

5v + 12.5

We know that momentum before firing = momentum after firing

=> 5v + 12.5 = 0

=> 5v = -12.5

=> v = -12.5/5

=> v = -2.5m/s

Hence the recoil velocity of gun is -2.5m/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.