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Answer :
Final answer:
The resultant velocity of the guy and the sledge is 0 m/s.
Explanation:
The resultant velocity can be calculated using the principle of conservation of momentum. The initial momentum of the guy and the sledge is zero since they are at rest. When the bullet is discharged, it gains momentum in the positive-x direction. Therefore, the guy and the sledge will have an equal but opposite momentum in order to conserve momentum.
The momentum of the bullet can be calculated as p = mv, where m is mass and v is velocity. Given that the mass of the bullet is 84g (0.084kg) and the muzzle velocity is 709m/s, the momentum of the bullet is 0.084kg * 709m/s = 59.556kg*m/s. In order to conserve momentum, the combined momentum of the guy and the sledge must be -59.556kg*m/s. Using the formula p = mv, where m is mass and v is velocity, we can solve for the resultant velocity.
Let 'v' be the resultant velocity. The guy has a mass of 71kg and the sledge has a mass of 97kg. Therefore, the combined mass of the guy and the sledge is 71kg + 97kg = 168kg.
The resultant velocity can be calculated as: (-71kg * v) + (-97kg * v) = -168kg * 0
Simplifying the equation, we get: -168v = 0
Dividing by -168, we find that the resultant velocity is v = 0 m/s.
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