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A frictionless tube is bent into the shape of a semicircle with radius R. The semicircle is tilted so that its diameter makes a


 

A frictionless tube is bent into the shape of a semicircle with radius R. The semicircle is tilted so that its diameter makes a fixed angle with respect to the vertical. A small mass is released from rest at the top of the tube and slides down through it. When the mass leaves the tube, it undergoes projectile motion without any resistance. Led D be the distance traveled horizontally from the launcher up to the time when the mass returns to the height it had when it left the tube. What should be so that D is as large as possible? R D

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