Question

a hunter fires a bullet of mass 10 g with the velocity of 400m/s from a gun mass 5kg what will be the recoil velocity

Answer 1

here no external force is acted (neglect air resistant) hence momentum of system(gun+bullet) is conserved 

initial momentum = finial momentum

let the recoil velocity of gun = v

0.01*0 + 4*0 = 0.01*400 + 4*v

v = -1m/s

hence gun recoil with velocity 1m/s 

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Answer 2

We have,
m1,mass of bullet = 10/1000kg=0.01kg
m2,mass of gun = 5kg
v1, velocity of bullet = 400m/s
v2, recoil velocity of gun = ?
Now,
According to law of conservation of momentum,
Momentum of bullet = Momentum of gun
m1*m2 = m2*v2
0.01*400 = 5*v2
4 = 5*v2
v2 = 4/5
v2 = 0.8m/s

So, the recoil velocity of gun is 0.8m/s