A 95 kg man standing on a surface of negligible friction shoves a 74 g stone lying at his feet, giving it a velocity of 4.0 m/s. What velocity does the man acquire as a result?

This problem can be solved using the principle of conservation of momentum. The total momentum before the man shoves the stone is equal to the total momentum after he shoves the stone.

Step 1: Convert the mass of the stone to kg, because the man's mass is given in kg. So, 74 g = 0.074 kg.

Step 2: Calculate the total initial momentum before the shove. Since both the man and the stone are initially at rest, the total initial momentum is 0.

Step 3: Calculate the final momentum of the stone after the shove. This is done by multiplying the mass of the stone by its final velocity. So, the final momentum of the stone is 0.074 kg * 4.0 m/s = 0.296 kg*m/s.

Step 4: Since the total momentum must be conserved, the final momentum of the man must be equal to the negative of the final momentum of the stone (because they move in opposite directions). So, the final momentum of the man is -0.296 kg*m/s.

Step 5: Finally, calculate the final velocity of the man by dividing his final momentum by his mass. So, the final velocity of the man is -0.296 kg*m/s / 95 kg = -0.00312 m/s.

Therefore, the man acquires a velocity of -0.00312 m/s as a result of shoving the stone. The negative sign indicates that the man moves in the opposite direction to the stone.

This problem can be solved using the principle of conservation of momentum. The total momentum before the man shoves the stone is equal to the total momentum after he shoves the stone.

Step 1: Convert the mass of the stone to kilograms, since the man's mass is given in kilograms. 74 g = 0.074 kg

Step 2: Calculate the total initial momentum before the shove. Since both the man and the stone are initially at rest, the total initial momentum is 0.

Step 3: Calculate the final momentum of the stone after the shove. Momentum = mass x velocity Momentum of the stone = 0.074 kg x 4.0 m/s = 0.296 kg*m/s

Step 4: Calculate the final momentum of the man. According to the principle of conservation of momentum, the total momentum before the shove (which is 0) is equal to the total momentum after the shove. Therefore, the momentum of the man is equal to the negative of the momentum of the stone (since they move in opposite directions). Momentum of the man = - Momentum of the stone = -0.296 kg*m/s

Step 5: Calculate the velocity of the man. Velocity = Momentum / mass Velocity of the man = -0.296 kg*m/s / 95 kg = -0.00312 m/s

Therefore, the man acquires a velocity of -0.00312 m/s as a result of shoving the stone. The negative sign indicates that the direction of the man's velocity is opposite to the direction of the stone's velocity.