#21

Read 6.2
6.2; 4(non-negative x and y is important; why?), 13, 20, 30, 32, 40, 42.
Hint on 13: think of energy "cost" by using relative cost/mile where cost/mile on land is 1.

*Optional Star:  Do two more problems: 6.2; 44 and the following Problem A: 
Not only dogs know calculus but light does too!  When light hits water it bends because it moves faster in air than in water.  The angle is given by Snell's Law shown on p. 116.  Derive this law by minimizing the total time for light to go from start to finish.  From upper left point to lower right, label constants for the vertical distances through Medium 1 and Medium 2 and the total horizontal distance.  The variable is the horizontal distance x in Medium 1.  Take derivative of total time and set it equal to zero.  Do not solve for x but, instead, interpret the ratios as trigonometric functions and rewrite as Snell's Law.