An astronaut, mass 128.2 kg including
spacesuit, pushes off from the
International Space Station (mass 110 tons) with a speed of 1.2 m/s. What is the speed of the Space station in the opposite direction? Use 2 s f. for your answer
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To find the speed of the space station in the opposite direction, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
Here, the momentum of the astronaut and the space station will be conserved. The momentum of an object is given by the product of its mass and velocity.
Before the astronaut pushes off, the total momentum is zero because both the astronaut and the space station are at rest. Therefore, the total momentum after the push off must also be zero to satisfy the conservation of momentum.
Let's denote the velocity of the space station in the opposite direction as v (m/s). The momentum of the astronaut after the push off is given by (mass of the astronaut) x (velocity of the astronaut), while the momentum of the space station is given by (mass of the space station) x (velocity of the space station).
Using the principle of conservation of momentum, we can write the equation:
0 = (mass of the astronaut) x (velocity of the astronaut) + (mass of the space station) x (velocity of the space station)
Substituting the known values:
0 = (128.2 kg) x (1.2 m/s) + (110 tons) x (v)
Now we can solve for v:
0 = 154.44 kg·m/s + (110 × 1000 kg) x (v)
Rearranging the equation:
-154.44 kg·m/s = 110,000 kg x (v)
Dividing both sides by 110,000 kg:
-154.44 kg·m/s / 110,000 kg = v
Simplifying:
-0.001404 m/s = v
Therefore, the speed of the space station in the opposite direction is approximately -0.0014 m/s (keep in mind that the negative sign indicates the opposite direction of the astronaut's motion).
Answer: The speed of the Space station in the opposite direction is approximately -0.0014 m/s.