Question 3: Chapter 3, Problem 42 from Serway. This also appears on your written homework. What does it mean for an object to move upstream? What about downstream? You need to be sure you understand these before you can work this problem. It will definitely help to draw diagrams for this problem.
A river has a steady speed of vs. A student swims upstream a distance d (measured along the bank of the river) and back to their starting point. (a) If the student can swim at a speed of v in still water, how much time, tup, does it take the student to swim upstream a distance d? Express the answer in terms of d, v, and vs. (b) Using the same variables (v, vs, and d), how much time, tdown, does it take to swim back downstream to the starting point? (c) Sum the answers found in parts (a) and (b) and show that the total time, ta, required for the whole trip can be written as
(d) How much time, tb, does the trip take in still water? (e) Which is larger, ta or tb ? Is it always larger? Justify your answer algebraically.