Chapter 4.7, Problem 41E

Minimum Time A man is in a boat 2 miles from the nearest point on the coast. He is traveling to a point Q, located3 miles down the coast and 1 mile inland (see figure), (a) The man rows at 2 miles per hour and walks at 4 miles per hour. Toward what point on the coast should he row in order to reach point 0 in the least time? (b) The man rows at v, miles per hour and walks at v, miles per hour. Let ${\theta }_1$ and ${\theta }_2$ be the magnitudes of the angles. Show that the man will reach point Q in the least time when $(\sin {\theta }_1)/v_1=(\sin {\theta }_2)/v_2$.