A car with a gun mounted on it is kept on horizontal friction less surface. Total mass of car, gun and shell is $50 k g$ . Mass of each shell is $1 k g$ . If shell is fired horizontally with relative velocity $100 m / s e c$ with respect to gun . What is the recoil speed of car after second shot in nearest integer?

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Solution

Centre of mass of velocity of shell = 0 (initially at rest)
Therefore , 0 = 49 m x V + m x 200
V = -200/49 m/s
200/49 m/s towards left .
Another shell is fire , then the velocity of the car , with respect to platform is
V' = 200/49 m/s towards left
Another shell is fired , then the velocity of the car with respect to platform is
v' = 200/48 m/s towards left
Now , the velocity of the car with respect to earth is (200/49 + 200/48) = 19400/2352 = 8.24 m/s towards left.

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