A 10kg gun fires a bullet of 100g with a speed of 200m/s relative to the barrel of the gun, which is inclined at an angle 45∘ with the horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun (in m/s). (Answer upto two decimal places)
A
1.39
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B
1.4
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C
1.40
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Solution
Let the recoil velocity of the gun in negative direction = −vm/s
Horizontal velocity of bullet V1=200cos45∘=200√2=100√2m/s
Given, mass of gun, M=10kg
and mass of bullet, m=0.1kg
Applying conservation of linear momentum in horizontal direction :- m(100√2−v)+M(−v)=0 0.1(100√2−v)=10×v v=100√2×0.110.1=1.4m/s ∴v=1.4m/s is the recoil velocity of the gun.