64. Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation [v dv = - GMS 1/2 dy where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation v² = √² + 2GM (1 - 1) y R where vo is the initial velocity of the object and R is the radius of Earth.

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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!