Newtons law of gravity says that the gravitational forcebetween two bodies is attractive

Chapter 6, Problem 38

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Newtons law of gravity says that the gravitational forcebetween two bodies is attractive and given byF = GMmr2 ,where G is the gravitational constant, m and M are themasses of the two bodies, and r is the distance betweenthem. This is the famous inverse square law. For a fallingbody, we take M to be the mass of the earth and r to bethe distance from the body to the center of the earth. So,actually, r changes as the body falls, but for anything wecan easily observe (say, a ball dropped from the Tower ofPisa), it wont change significantly over the course of themotion. Hence, as an approximation, it is reasonable toassume that the force is constant. According to Newtonssecond law, acceleration is caused by a force andForce = Mass Acceleration.(a) Find the differential equation for the position, s of amoving body as a function of time.(b) Explain how the differential equation shows the accelerationof the body is independent of its mass.

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