PROBLEMS FROM SERWAY 
        
        
        CHAPTER 5
        
        
        46. A ball is suspended from the ceiling of a moving car
            by a string 25 cm in length.  An observer in the car
            notes that the ball deflects 6 cm from the vertical
            toward the rear of the car.  What is the acceleration
            of the car?
        
        CHAPTER 12 
        
        
        17.  A spaceship is fired from the Earth's surface with an
             initial speed of 20,000 m/s.  What will its speed be
             when it is very far from the Earth?  (Neglect friction.)

        41.  Two hypothetical planets of masses m1 and m2 and radii 
             r1 and r2, respectively, are at rest when they are an
             infinite distance apart.  Because of their gravitational
             attraction, they head toward each other on a collision
             course.  (Hint:  Note that both energy and momentum are
             conserved.)
        
             (a)  When their center-to-center separation is d, find
             the speed of each planet and their relative velocity.
        
             (b)  Find the kinetic energy of each planet just before
             they collide if m1 = 2 x 10^24 kg, m2 = 8 x 10^24 kg,
             r1 = 3 x 10^6 m, and r2 = 5 x 10^6 m.
        
        48.  (a)  Determine the amount of work (in joules) that must
             be done on a 100 kg payload to elevate it to a height
             of 1000 km above the Earth's surface.
        
             (b)  Determine the amount of additional work that is
             required to put the payload into circular orbit at this
             elevation.