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A gun of mass 'M’ fires a bullet of mass 'm’ horizontally. The energy of firing is such that it is sufficient to project the bullet vertically to a height 'h’. What is the recoil velocity of the gun?

A gun of mass 'M’ fires a bullet of mass 'm’ horizontally. The energy of firing is such that it is sufficient to project the bullet vertically to a height 'h’. What is the recoil velocity of the gun?

Grade:12

3 Answers

Adarsh
768 Points
6 years ago
Dear Aryaman,
The energy required to project bullet vertically to a height h will be equal to the kinetic energy of gun after firing..
so ,   ½Mv2=mgh  => v =2mgh/M
Thanks and Regards
Adarsh
Khimraj
3007 Points
6 years ago
Let velocity of bullet is v and recoil velocity of gun is V.energy of firing is such that it is sufficient to project the bullet vertically to a height 'h’.
Then ½mv2 = mgh.
So v = (2gh)1/2
From conservation of linear momentum
MV = mv
So V = mv/M = (m/M)*(2gh)1/2.
Hope it clears.
Namratha
13 Points
3 years ago
Let v be the velocity of the bullet & V be the recoil velocity of gun.
mv + M (-V) = 0 
v=MV/m
E= 1/2mv^2 + 1/2MV^2
mgh = 1/2 m( MV/m)^2 + 1/2MV^2 
On solving we get,
V = (2m^2gh/M (m+M))^1/2
 

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