PROBLEMS FROM SERWAY - CHAPTERS 1 AND 3
        
        
        CHAPTER 1
        
        42. A person walks along a circular path of radius 5 m,
            around one half of the circle.  (a) Find the magnitude
            of the displacement vector.  (b) How far did the person
            walk?  (c) What is the magnitude of the displacement
            if the circle is completed?
        
        CHAPTER 3
        
         3. A motorist drives south at 20 m/s for 3 min, then
            turns west and travels at 25 m/s for 2 min, and finally
            travels northwest at 30 m/s for 1 min.  For this 6-min
            trip, find (a) the net vector displacement of the
            motorist, (b) the motorist's average speed, and (c) the
            average velocity of the motorist.
        
        62. After delivering his toys in the usual manner, Santa
            decides to have some fun and slide down an icy roof.
            The roof is 8 m in length and makes an angle of 37 
            degrees with the horizontal.  He starts from rest at the 
            top of the roof and accelerates at the rate of 5 m/s^2.
            The edge of the roof is 6 m above a soft snowbank, on
            which Santa lands.  Find (a) Santa's velocity 
            components when he reaches the snowbank, (b) the total
            time he is in motion, and (c) the horizontal distance
            d between the house and the point where he lands in the
            snow.

        65. A hawk is flying horizontally at 10.0 m/s in a straight
            line, 200 m above the ground.  A mouse it has been
            carrying is released from its grasp.  The hawk continues
            on its path at the same speed for 2 seconds before
            attempting to retrieve its prey.  To accomplish the
            retrieval, it dives in a straight line at constant speed
            and recaptures the mouse 3.0 m above the ground.
            (a)  Assuming no air resistance, find the diving speed
            of the hawk.  (b) What angle did the hawk make with the
            horizontal during its descent?  (c) For how long did
            the mouse "enjoy" free fall?