A gun of mass 5kg fire a bullet of mass 5g vertically upward to a height of 100m. Calculate the recoil velocity of the gun.
A gun of mass 5kg fire a bullet of mass 5g vertically upward to a height of 100m. Calculate the recoil velocity of the gun.
The bullet attains the maximum height of 100 m after fired.
If the bullet fired with initial velocity u.
Then, at the height of 100 m, the final velocity of bullet v
From third equation of motion
v^2 = u^2+2gH
g is negative, because the motion is upwards.
0 = u^2 -2×10×100
So, u = 44.72 m/sec
Now, from the conservation of momentum-
Initial momentum of the system including the gun and the bullet = 0
Final momentum of the system = momentum of the gun + momentum of the bullet
= MgVg+ MbVb
= 5×Vg+ 5/1000×44.72 (5 g = 5/1000 kg)
So, the recoil velocity of gun, Vg = -0.044 m/sec(answer)
The negative sign shows that the direction of recoil velocity is opposite of bullet velocity.
The bullet attains the maximum height of 100 m after fired.
If the bullet fired with initial velocity u.
Then, at the height of 100 m, the final velocity of bullet v
From third equation of motion
v^2 = u^2+2gH
g is negative, because the motion is upwards.
0 = u^2 -2×10×100
So, u = 44.72 m/sec
Now, from the conservation of momentum-
Initial momentum of the system including the gun and the bullet = 0
Final momentum of the system = momentum of the gun + momentum of the bullet
= MgVg+ MbVb
= 5×Vg+ 5/1000×44.72 (5 g = 5/1000 kg)
So, the recoil velocity of gun, Vg = -0.044 m/sec(answer)
The negative sign shows that the direction of recoil velocity is opposite of bullet velocity.
