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Answer :
Final answer:
The distance between the astronaut and the satellite after 11.0 min is 457,584 m.
Explanation:
To find the distance between the astronaut and the satellite after 11.0 min, we can first calculate the initial velocity of the astronaut and satellite using the forces involved. Since the astronaut pushes off the satellite, the force exerted on the satellite and the astronaut will be equal in magnitude but opposite in direction. We can use Newton's second law, F = ma, to calculate the acceleration of the satellite.
First, let's calculate the initial velocity of the astronaut:
F = ma
a = F/m = 90.0 N / 93 kg = 0.968 m/s²
Now, we can calculate the initial velocity of the satellite:
a = F/m = -90.0 N / 645 kg = -0.140 m/s²
The initial velocity of the satellite is negative because it is moving in the opposite direction of the astronaut.
To find the distance between the astronaut and the satellite after 11.0 min, we can use the equation of motion:
d = (vf - vi)t
Where:
d = distance
vf = final velocity
vi = initial velocity
t = time
First, let's calculate the final velocity of the astronaut:
vi = 0 m/s (since the astronaut starts from rest)
t = 11.0 min = 660 s
vf = vi + at = 0 + 0.968 m/s² * 660 s = 638.88 m/s
Next, let's calculate the final velocity of the satellite:
vi = 0 m/s (since the satellite starts from rest)
vf = vi + at = 0 + (-0.140 m/s²) * 660 s = -92.40 m/s
Finally, let's find the distance between the astronaut and the satellite:
d = (vf - vi)t = (638.88 m/s - (-92.40 m/s)) * 660 s = 457,584 m
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