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An astronaut of mass 70 kg carries an empty oxygen tank of mass 14 kg. He throws the tank away from himself with a speed of 3 m/s. With what velocity does the astronaut start to move through space?
To find the velocity at which the astronaut starts to move through space, we can use the principle of conservation of momentum. The total momentum before the throw is equal to the total momentum after the throw.
The momentum of an object is calculated by multiplying its mass with its velocity. Hence, the initial momentum of the astronaut with mass 70 kg can be given as follows:
Initial momentum of astronaut = Mass of astronaut * Initial velocity of astronaut
Since the astronaut starts from rest (initial velocity is 0), the initial momentum of the astronaut is 0 kg m/s.
The momentum of the oxygen tank is calculated similarly, using its mass and velocity. The final momentum of the astronaut and the oxygen tank combined is zero, as they both have negligible mass compared to the tank.
Final momentum of the astronaut + Final momentum of the tank = 0 kg m/s
Now, we can set up the equation using the principle of conservation of momentum:
Initial momentum = Final momentum
0 kg m/s = (Mass of the astronaut * Final velocity of the astronaut) + (Mass of the tank * Final velocity of the tank)
Substituting the given values:
0 kg m/s = (70 kg * Final velocity of the astronaut) + (14 kg * 3 m/s)
Now, we can solve for the final velocity of the astronaut.
0 kg m/s = 70 kg * Final velocity of the astronaut + 42 kg m/s
Rearranging the equation:
-42 kg m/s = 70 kg * Final velocity of the astronaut
Dividing both sides by 70 kg:
Final velocity of the astronaut = -42 kg m/s / 70 kg
Final velocity of the astronaut ≈ -0.60 m/s
Therefore, the velocity at which the astronaut starts to move through space is approximately -0.60 m/s. The negative sign indicates that the astronaut moves in the opposite direction of the oxygen tank's throw.