When the gun is fired horizontally :
m = mass of each bullet = 4.20 g = 0.0042 kg
v = velocity of the bullet after fire = 965 m/s
M = mass of the hunter including gun = 72.5 kg
V = velocity of hunter including gun after fire = ?
V' = velocity of the combination of bullet , gun and hunter before fire = 0 m/s
Using conservation of momentum
m v + M V = (m + M) V'
(0.0042) (965) + (72.5) V = (0.0042 + 72.5) (0)
V = - 0.056 m/s
so recoil velocity comes out to be 0.056 m/s
When the gun is fired at angle 56.0⁰ above the horizontal :
m = mass of each bullet = 4.20 g = 0.0042 kg
v = velocity of the bullet after fire = 965 Cos56 = 539.62 m/s
M = mass of the hunter including gun = 72.5 kg
V = velocity of hunter including gun after fire = ?
V' = velocity of the combination of bullet , gun and hunter before fire = 0 m/s
Using conservation of momentum
m v + M V = (m + M) V'
(0.0042) (539.62) + (72.5) V = (0.0042 + 72.5) (0)
V = - 0.031 m/s
so recoil velocity comes out to be 0.031 m/s
