Question

derive mathematical expression for recoil velocity of gun

Answer 1

HEY MATE

HERE IS YOUR ANSWER

RECOILING OF GUN

AS THE RECOILING OF GUN IS SAID TO BE AT THE POINT WHERE MOMENTUM INITIAL IT'S EQUAL MOMENTUM FINAL

Pi =Pf

mv=MV.

where
m IS MASS OF BULLET
v IS VELOCITY OF BULLET
M IS MASS OF GUN
V IS VELOCITY OF GUN

mv=MV

V=mv/M


HOPE IT WELL HELP U

Answer 2

When a bullet is fired from a gun, the gun moves in a direction opposite to the direction of motion of the bullet, which is called recoil of the gun. Let m and M be the masses of the bullet and the gun respectively. Initial velocities of both are zero and after firing let the velocities of the bullet and gun be v and V respectively.
So, total linear momentum before firing =0
Vector sum of linear momenta after firing = mv +MV
So, following principle of conservation of linear momentum,
mv +MV =0
So,V= - m/M ×v
V is the recoil velocity and the negative sign shows that V is opposite in direction to that of v.