**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 and its recoil velocity is the mass of the bullet is and it is shooted by the gun with the velocity of . Since the initialy bullet and gun both are in rest before the bullet is fired, therefore the intial velocity of gun, and initial velocity of the bullet .**

**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**

**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, = 4 kg, Initial velocity of the gun, , Mass of bullet, = 50 gm = 0.05 kg, Initial velocity of the bullet, , Final velocity of the gun (recoil velocity of gun),, Final velocity of bullet ,**

**= –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?**

**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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