A river has a steady speed of vs. A student swims upstream a distance d and back

Question

A river has a steady speed of vs. A student swims upstream a distance d and back to the 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. up (b) Using the same variables, how much time tdown does it takes to swim back downstream to the starting point? town = (c) Sum the answers found in parts (a) and (b) and show that the time ta required for the whole trip can be written as (Do this on paper. Your instructor may ask you to turn in this work.) (d) How much time tb does the trip take in still water? (Use the following as necessary: d and v.)

Explanation / Answer

the speed of the student relative to shore is

v_ up = v- vs

v _down = v+ vs

The time required to travel distance d upstream
is

t_up = d/ v_up = d/ v- vs

(2)

The time required to swim the same distance d downstream is

t_down = d/ v_down = d/ v+ vs

(c)

t_d = t_up + t_down

= d/ v- vs+d/ v+ vs

= d(v+ vs)+ d( v- vs)/ ( v- vs) ( v+ vs)

= 2dv/ v^2 - vs^2

= 2d/v/ 1- vs^2/v^2

(d)

in still water vx= 0 and the time for the comple tripe is

tb = ta = 2d/v/ 1- o/v^2 = 2d/v

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