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Hi there.
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So for this problem, we are told that a father fashions a swim for his children out of a long rope that he fastens to the limp of a tall three.
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Now, as one of the children swims from this rope that is 8 .40 meters long, his tendential speed at the bottom of the swim is 7 .35 meters per second.
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So the first question is to obtain what is the centripetal acceleration in meters per second square of the child at the bottom of the swim.
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Now, as you can see from the figure, the child describe a path that is circular.
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So in that sense, we can obtain the centripetal acceleration by just dividing the speed to the square over the radius.
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Which in this case the radius corresponds to the length of the rope.
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So we just simply substitute the values into this expression.
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So we have 7 .35 meters per second to the square, and this divided by the radius, which in this case is 8 .4 meters...