EXAM 1                  March 11, 1993             PS 207                      
                                                                               
      If you need a constant not given here or do not understand a             
problem, please ask me about it.  Remember to include diagrams and             
explain your reasoning.  No notes, books, etc. may be used.                    

                                         2            2
                            g = 9.8 m/sec  = 32 ft/sec                       
                                                                               
                                     -31                                       
The mass of the electron is 9.11 x 10    kg                                    

                                    6                                          
The radius of the earth is 6.38 x 10  m                                        

      1. (10 points).  State and explain how to remember (not             
necessarily derive):                                                        

         a.  The relation for the position of a particle as a            
function of time for motion in one dimension with constant                     
acceleration.                                                              

         b.  The relation giving the magnitude of the centripetal        
acceleration for a particle moving at constant speed   v  in a circle of
radius  R .                                                         


      The remaining problems count 30 points each.  A diagram is        
required for each problem.                                             

      2.  (From homework).  An object on the equator has an                
acceleration toward the center of the earth because of the earth's             
rotation.  Calculate the magnitude of this acceleration and express it         
as a fraction of the free-fall acceleration  g .                     

      3.  Two trains are headed toward each other on the same track          
with equal speeds of 20 m/s.  When they are 2 km apart, they see each          
other and begin to decelerate.  If their decelerations are uniform and         
equal, how large must the decelerations be if the trains are to barely         
avoid collision?                                                             
                                                                           
      4. a.  Show that if a projectile goes up through any height and     


comes back to that height a time  T   later, then the y-component of its
                                   A

velocity at that height is  v = +- gT / 2 .
                             y       A

         b. [Do this last]  Show that if the same projectile also         

spends a time T   at or above a line a distance  h above the first,  
               B
g  may be determined by                                                    


                         8h
                g = ---------------
                       2       2
                     T   -  T
                      A      B