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Imagine a roller coaster that starts at the top of a big hill, and goes immediately...

Imagine a roller coaster that starts at the top of a big hill, and goes immediately into a loop-the-loop. If the mass of you and the cart is 50 kg, and the loop is 30 m tall, how high does the hill have to be so that you make it through the loop without falling off? Assume there is no friction. Be exact in your calculation.

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