If the ratio of the initial velocity to the velocity back to the throwing point is k, and the air resistance is constant during the motion, the ratio of gravity to resistance is K______ ．

Let the mass of the object be m, the air resistance be f, and the maximum height of rising be H. according to the kinetic energy theorem, we can get the ascending process: - (Mg + F) H = 0-12mv20, the descending process: (Mg-F) H = 12mv2. From the simultaneous solution of the problem, v0v = k, we can get MGF = K2 + 1k2 − 1, so the answer is: K2 + 1k2 − 1

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