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Answer :
Final answer:
When the astronaut's speed reaches 70 m/s, the length of the lifeline would be approximately 668.34 meters.
Explanation:
This problem can be solved using the principles of circular motion. The velocity of an object moving in a circle of radius r with n revolutions per unit of time is given by v = 2πrn. The astronaut initially moves at a speed of v1 = 2π*134*5/60 m/s.
Now, we need to find the radius (r2) when the speed is 70 m/s, which we can calculate as r2 = v2 / (2πn) = 70 / (2π*5/60). We find that the radius (or the length of the lifeline) at this speed is approximately 668.34 meters.
Learn more about Circular Motion here:
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