Aperson holding a 15.0 kg containing one 50.0 g bullet is riding on a train that is traveling at 75.0 km/h east. if the man fires the gun and the bullet moves with a velocity of 350 m/s east(relative to the train), what is the velocity of the gun relative to the ground

The velocity of the gun relative to the ground is 19.73 m/

The given parameters;

Apply the principle of conservation of linear momentum, to determine the velocity of the gun relative to the ground;

Thus, the velocity of the gun relative to the ground is 19.73 m/s.

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The velocity of the gun relative to the ground is 19.66 m/s

Explanation:

Given data,

The mass of the gun, M = 15.0 kg

The mass of the bullet, m = 50 g

The velocity of the train, v = 75 km/h

                                           = 20.83 m/s

The velocity of bullet relative to train, V' = 350 m/s

The velocity of bullet relative to ground, V = 350 + 20

                                                                       = 370 m/s

According to the law of conservation of momentum,

                                Mv' + mV' = 0

                                      = -1.17 m/s

Therefore, the velocity of the gun with,

                                   v₀ = V + v'

                                        = 20.83 - 1.17

                                         = 19.66 m/s

Hence, the velocity of the gun relative to the ground is 19.66 m/s

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