Evaluation of recoil velocity of the gun

CBSE Class IX science has 5 lessons, among them ‘Force and laws of motion‘ is very important, in this lesson you will study Newton’s law of motion, force, momentum and conservation of momentum. Momentum is the product of mass and velocity. Although there are so many applications of conservation of momentum. One of the applications based on conservation of momentum is when a bullet is fired by a gun then gun moves in the backward direction with a velocity known as recoil velocity of the gun, actually the gun exerts a force to the bullet, the bullet gains a large momentum which causes the bullet move in the forward direction with large velocity and the same momentum is transferred to the gun, gun acquires a momentum due to which it gains a velocity which is recoil velocity of the gun. Here we are going to discuss how to evaluate the recoil velocity of the gun. After you study this post evaluation of the recoil velocity of the gun, at the end there are given few unsolved questions which you can solve easily. If you like our this post, please don’t forget to subscribe to our website and make comment.

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When a bullet is shooted by a gun then determine the recoil velocity of the gun. We can understand how to evaluate recoil Velocity of gun by the following way.

Let the mass of gun is $\boldsymbol{M_{1}}$ and its recoil velocity is $\boldsymbol{V_{1}}$ the mass of the bullet is $\boldsymbol{M_{2}}$ and it is shooted by the gun with the velocity of $\boldsymbol{V_{2}}$ . Since the initialy bullet and gun both are in rest before the bullet is fired, therefore the intial velocity of gun, $\boldsymbol{U_{1}=0}$ and initial velocity of the bullet $\boldsymbol{U_{2}=0}$ .

As we know the momentum = mass × velocity, According to the conservation of momentum

Initial momentum = Final momentum

The initial velocity of the gun ×mass of the gun + Initial velocity of bullet × mass of bullet = Final velocity of the gun ×mass of the gun + Final velocity of the bullet × mass of the bullet.

The final velocity of the gun = Recoil velocity of the gun

$\boldsymbol{U_{1} M_{1}+U_{2} M_{2}=V_{1} M_{1}+V_{2} M_{2}}$

$\boldsymbol{0\times M_{1}+0\times M_{2}=V_{1} M_{1}+V_{2} M_{2}}$

$\boldsymbol{V_{1}M_{1}=-V_{2}M_{2}}$

$\boldsymbol{{V_{1}=-\frac{V_{2}M_{2}}{M_{1}}}}$

The negative sign of velocity shows that the gun moves in the opposite direction of the bullet.

Similar question.

From a gun of mass 4 kg. A bullet of mass 50 gm is fired with an initial velocity of 35 m/s. Calculate the recoil velocity of the gun.

Ans. Mass of gun, $\boldsymbol{M_{1}}$ = 4 kg, Initial velocity of the gun, $\boldsymbol{U_{1}=0}$ , Mass of bullet, $\boldsymbol{M_{2}}$ = 50 gm = 0.05 kg, Initial velocity of the bullet, $\boldsymbol{U_{2}=0}$ , Final velocity of the gun (recoil velocity of gun), $\boldsymbol{V_{1}}$ , Final velocity of bullet , $\boldsymbol{V_{2}=35\: m/s}$

$\boldsymbol{{V_{1}=-\frac{V_{2}M_{2}}{M_{1}}}}$

$\boldsymbol{= -\frac{35\times 0.05}{4}}$

= –0.4375≈– 0.44

Hence the recoil velocity of the gun =– 0.44 m/s, its meaning is that after the bullet is fired, the gun moves in the backward direction with the velocity of 0.44 m/s.

You can get the help of video in understanding the solution of the question

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You can solve other similar questions based on the conservation of momentum as follows.

Q1. Find the recoil velocity of a gun having a mass equal to 8 kg, if a bullet of 40 gm acquires the velocity of 500m/s after firing from the gun.

Q2.A 35 Kg boy jumps (from rest) into a moving trolley of mass 70 Kg and already moving at a velocity of 5 m/s to the right. What is the speed of the trolley after the boy has jumped in?

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Q3.5 Kg gun fires a bullet of 15 grams at a velocity of 1000 m/s to the right. What is the velocity of the recoil of the gun?

Q4.6kg ball is thrown west at 20m/s and collides with a 14kg ball while in the air. If the balls stick together in the crash and fall straight down to the ground, what was the velocity of the second ball?

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Q5.2000kg car traveling at 25m/s rear-ends another 2000kg car at rest. The two bumpers lock and the cars move forward together. What is their final velocity?

Q6.900kg car strikes a 1000kg car at rest from behind. The bumpers lock and they move forward together. If their new final velocity is equal to 18m/s, what was the initial speed of the first car?

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Q7.10kg ball moving at 30ms strikes a 12kg ball at rest. After the collision, the 10kg ball is moving with a velocity of 13m/s. What is the velocity of the second ball after the collision?

Q8.11kg ball moving at 33m/s strikes a second ball at rest. After the collision, the 11kg ball is moving with a velocity of 13m/s and the second ball is moving with a velocity of 8ms. What is the mass of the second ball?

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