Suppose you fire a projectile straight up from the Earth’s NorthPole with a speed of 10.5km/s. Ignore air resistance. (a) How farfrom the center of the Earth does the projectile rise? How highabove the surface of the Earth is that? (The radius of the Earth isRE = 6.37 × 106 m, and the mass of the Earth is M = 5.97 × 1024kg.) (b) How different is the result you got in part (a) above fromwhat you would have obtained if you had treated the Earth’sgravitational force as a constant (independent of height), as wedid in previous chapters? (c) Using the correct expression for thegravitational potential energy, what is the total energy of theprojectile-Earth system, if the projectile’s mass is 1, 000 kg? Nowassume the projectile is fired horizontally instead, with the samespeed. This time, it actually goes into orbit! (Well, it would, ifyou could neglect things like air resistance, and mountains andstuff like that. Assume it does, anyway, and answer the followingquestions:) (d) What is the projectile’s angular momentum aroundthe center of the Earth? (e) How far from the center of the Earthdoes it make it this time? (You will need to use conservation ofenergy and angular momentum to answer this one, unless you canthink of a shortcut. . .) (f) Draw a sketch of the Earth and theprojectile’s trajectory.