PROBLEMS TO BE WRITTEN UP AND TURNED IN AT RECITATION

     These 3 problems are due at your first recitation meeting after 
     Mon. 11/29.  Each problem should be written on a single sheet 
     of paper (you may use front and back if necessary); the three sheets
     should then be stapled together.  Please order your sheets in the
     order below.  For full credit, the work must be neat, with symbols 
     defined in clearly labeled diagrams.  The labels must be in BOTH 
     words and symbols.  For each part of each problem, you must BRIEFLY 
     explain your strategy in words, as well as neatly showing your 
     physics equations and math, with proper units. 
     
       #1 FISHBANE - CHAPTER 12 - PROBLEM 35  (10 points)
         A small package is fired off Earth's surface with a speed v at a 
         45 degree angle with the local horizontal.  It reaches a maximum 
         height h above the surface at h = 6370 km, a value equal to Earth's 
         radius itself.  What is its speed when it reaches this height?  
         Ignore any effects that might come from Earth's rotation or from 
         air resistance.  (Hint: You will need to use two conservation 
         equations and solve two equations in two unknowns.) 

       #2 FISHBANE - CHAPTER 12 - PROBLEM 55  (10 points)
         The Little Prince (a character in a book by Antoine de Saint-
         Exupery) lives on the spherically symmetric asteroid B-612.  The 
         density of B-612 is 5200 kg/cubic meter.  Assume that the asteroid 
         does not rotate.  The Little Prince noticed that he felt lighter 
         whenever he walked quickly around the asteroid.  In fact, he found 
         that he became weightless and started to orbit the asteroid like a 
         satellite whenever he speeded up to 2 m/s.  (a) Estimate the radius 
         of the asteroid from these data.  (b) What is the escape speed for 
         the asteroid?  (c) Suppose that B-612 does rotate about an axis 
         such that the length of the day there is 12 h.  Can the Little 
         Prince take advantage of this rotation when he wants to orbit the 
         asteroid?  What is his minimum ground speed for orbit in this case?

       #3 SERWAY - CHAPTER 12 - PROBLEM 49  (5 points)
        (The figure for this problem is similar to Fig. 9-35 on page 235 
         of Wolfson, except that the two objects are of different mass; 
         therefore, the more massive object is closer to the center of 
         mass, i.e in a smaller orbit.) Two stars of masses m1 and m2, 
         separated by a distance of d, revolve in circular orbits about 
         their center of mass.  Show that each star has a period given by

                    T^2 = (4pi^2)d^3/G(m1+m2)
         
        (Hint: Write Newton's 2nd Law for each star, make an appropriate
         substitution for the orbital speeds, add the two equations, and 
         use r2+r1 = d where r2 is the radius of the orbit of m2 and r1 
         is the radius of the orbit of m1.)