Quiz for Week 4 of PFP 96

You can (and in some cases should) use Maple to help solve the problems.

You can submit your results by e-mail or via FTP or on paper

1. Assuming Newton's Universal Law of Gravitation gives the gravitational force of any planet on a satellite in orbit around it as
   F = GM_Pm_sat/R_sat² where M_P is the mass of the planet, m_sat is the mass of the rock, R_sat is the radius of the orbit, and G is the universal constant 6.67 x 10^-11 N.m²/kg², find the potential energy of a geosynchronous satellite (i.e. one located 42.2 thousand kilometers above the earth) and mass of 1000 kg. Note: the earth's mass and radius are 5.98 x 10²⁴ kg and 6,370 kilometers, respectively.

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2. The figure below shows a cannon firing a cannonball so that it lands on a hillside that begins at the cannon's position. The cannon shoots the cannonball with a fixed velocity, v_c, at an adjustable angle of theta_c. If the angle of inclination of the hill is theta, find the the value of theta_c which maximizes the range of the cannonball along the hillside.