Suppose you fire a projectile straight up from the Earth’s North Pole with a speed of...

Suppose you fire a projectile straight up from the Earth’s North Pole with a speed of 10.5km/s. Ignore air resistance. (a) How far from the center of the Earth does the projectile rise? How high above the surface of the Earth is that? (The radius of the Earth is RE = 6.37 × 106 m, and the mass of the Earth is M = 5.97 × 1024 kg.) (b) How different is the result you got in part (a) above from what you would have obtained if you had treated the Earth’s gravitational force as a constant (independent of height), as we did in previous chapters? (c) Using the correct expression for the gravitational potential energy, what is the total energy of the projectile-Earth system, if the projectile’s mass is 1, 000 kg? Now assume the projectile is fired horizontally instead, with the same speed. This time, it actually goes into orbit! (Well, it would, if you could neglect things like air resistance, and mountains and stuff like that. Assume it does, anyway, and answer the following questions:) (d) What is the projectile’s angular momentum around the center of the Earth? (e) How far from the center of the Earth does it make it this time? (You will need to use conservation of energy and angular momentum to answer this one, unless you can think of a shortcut. . .) (f) Draw a sketch of the Earth and the projectile’s trajectory.

Expert Solution

genius_generous answered 1 year ago

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