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I have attached two very simple problems with their solutions. In the first problem the velocity of the mass center is not constant while in the second it is.

From my understanding, the mass center of a object that explodes continues to move as if the object had not exploded and if there are zero forces acting on it the velocity of the mass center is constant.

In problem 14.1 (the second page) the object has zero external forces, so I understand why the velocity is constant but in problem 14.16 (second page) we use the gravity acceleration to calculate the velocity of the oject even though there are zero external forces. Why do you consider the gravity in one problem and not in the other one?

Thanks.

From my understanding, the mass center of a object that explodes continues to move as if the object had not exploded and if there are zero forces acting on it the velocity of the mass center is constant.

In problem 14.1 (the second page) the object has zero external forces, so I understand why the velocity is constant but in problem 14.16 (second page) we use the gravity acceleration to calculate the velocity of the oject even though there are zero external forces. Why do you consider the gravity in one problem and not in the other one?

Thanks.