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?
I guess he and the tank were stationary when this text was written.
Therefore the initial momentum was zero.
Therefore the final momentum is zero, since there are no external forces mentioned.
70 + 14 = 84
initial momentum = 84 * 0 = 0
final momentum = 0 = 70 v + 14 * 3
v = -14 * 3 /70
The - sign means the astronaut moves in the opposite direction from the tank.
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces act on it.
The momentum of an object is given by the product of its mass and velocity. So, we can calculate the momentum of the astronaut and the tank separately.
The momentum of the astronaut before throwing the tank is given by:
Momentum of the astronaut before = mass of the astronaut × velocity of the astronaut before
Given that the mass of the astronaut is 70 kg and we need to find the velocity of the astronaut, let's call it V_a.
Now, let's calculate the momentum of the tank before it is thrown:
Momentum of the tank before = mass of the tank × velocity of the tank before
Given that the mass of the tank is 14 kg and the velocity of the tank before it is thrown is 0 m/s (since it's empty and at rest), we get:
Momentum of the tank before = 14 kg × 0 m/s = 0 kg m/s
According to the conservation of momentum, the total momentum before throwing the tank should be equal to the total momentum after throwing the tank. So:
Momentum before = Momentum after
(mass of the astronaut × velocity of the astronaut before) + (mass of the tank × velocity of the tank before) = (mass of the astronaut × velocity of the astronaut after) + (mass of the tank × velocity of the tank after)
Substituting the given values into the equation:
(70 kg × V_a) + (14 kg × 0 m/s) = (70 kg × V_a) + (14 kg × 3 m/s)
Simplifying the equation, we find:
70 kg × V_a = 70 kg × V_a + 14 kg × 3 m/s
Rearranging the equation to solve for V_a, we get:
0 = 14 kg × 3 m/s
Dividing both sides of the equation by 70 kg, we find:
0 = 3 m/s
Since the equation simplifies to 0 = 3 m/s, it means that there is no solution for the velocity of the astronaut after throwing the tank.