Question

find recoil velocity of a gun having mass equal to 10 kg ,if a bullet of 50 gm acquires the velocity of 600 m/s after firing from the gun​

Answer 1

Given :-  

• Mass of the bullet is 50 gm  = 0.050 kg ( m₁ )  
• Velocity of bullet before firing = 0 m/s ( u₁ )  
• Velocity of bullet after firing = 600 m/s ( v₁ )  
• Mass of the gun = 10 kg ( m₂ )  

• Velocity of gun before firing = 0 m/s ( u₂ )  

To  Find :-  

• Velocity of gun after firing ( Recoil velocity )  

Solution :-  

❒ Here, as we know that when we fire a gun the gun moves in the opposite direction of the bullet .  

$\underline{\sf{\dag} \;\; \mathfrak{As\;we\;know\;that:}}$  

$\bigstar$ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂  

 

Finding the recoil velocity :-  

→ ( 0.050 ×  0 ) + ( 10 ×  0 ) = ( 0.050  ×  600 ) + ( 10 × v₂)

→ ( 0 ) + ( 0 ) = ( 30 ) + ( 10 × v₂ )  

→ 0 = 30 + ( 10 × v₂ )  

→  ( 10 × v₂ ) = 0 - 30  

→  ( 10 × v₂ ) = -30  

→ v₂ = -30/10

→ v₂ = -3m/s

[ Note : Here, the velocity is negative because the bullet moves in the opposite direction as mentioned above ]  

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Hence,  

• The recoil velocity of the gun is 3 m/s  

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