3. The weight of a particle varies with altitude such that W = m(gr)/r², where ro is the radius of the earth and r is the distance from the particle to the earth's center. If the particle is fired vertically with a velocity vo from the earth's surface, determine its velocity as a function of position r. What is the smallest velocity vo required to escape the earth's gravitational field, what is the time required to reach the altitude?

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Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!