Question

from a rifle of mass 4 kg, a bullet
of mass 50 g is fired with an
Initial velocity of 35 m/s
Calculate the initial recoil velocity
of the rifle.​

Answer 1

Hey mate here is your solution

hope its correct

Answer 2

$\huge\star{\underline{\underline{\sf\purple{ Solution :-} }}}$

Given,

• Bullet’s mass (m1) = 50 g
• Rifle’s mass (m2) = 4kg = 4000g
• Initial velocity of the fired bullet (v1) = 35m/s

Solution:

Let the recoil velocity be $\sf{ v_{2} }$

Since the rifle was initially at rest, the initial momentum of the rifle = 0

Total momentum of the rifle and bullet after firing = $\sf{m_{1}v_{1}}$ + $\sf{m_{2}v_{2}}$

$\sf{ \hookrightarrow}$ As per the law of conservation of momentum,The total momentum of the rifle and the bullet after firing = 0

Therefore, $\sf{m_{1}v_{1}}$ + $\sf{m_{2}v_{2}}$ = 0

So,

Value after calculation;

$\\ \implies{\sf{ V^2 = - \dfrac{ m_{1}v_{1}}{m_{2}} }}$

$\implies{\sf{ - \dfrac{50g \times 35\:ms^{-1} }{4000g} }}$

$\implies{\boxed{\sf\purple{ - 0.4375\: ms^{-1} }}}$

Therefore,

The recoil velocity of the rifle is 0.4375 m/s.