Satellite path A satellite will travel in a parabolic path near a planet if its velocity

Chapter 10, Problem 10.66

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Satellite path A satellite will travel in a parabolic path near a planet if its velocity v in meters per second satisfies the equation , where r is the distance in meters between the satellite and the center of the planet and k is a positive constant. The planet will be located at the focus of the parabola, and the satellite will pass by the planet once. Suppose a satellite is designed to follow a parabolic path and travel within 58,000 miles of Mars, as shown in the figure on the next page. (a) Determine an equation of the form that describes its flight path.(b) For Mars, . Approximate the maximum velocity of the satellite.(c) Find the velocity of the satellite when its y-coordinate is 100,000 miles.