Two canoeists in identicalcanoes exert the same effort paddling and hencemaintai

Question

Two canoeists in identicalcanoes exert the

same effort paddling and hencemaintain the

same speed relative to thewater. One pad-

dles directly upstream (andmoves upstream),

whereas the other paddlesdirectly down-

stream. With downstream as thepositive

direction, an observer on shoredetermines

the velocities of the two canoesto be 1m/s

and 2.2 m/s, respectively.

What is the speed of the waterrelative to

shore? Answer in units ofm/s.

What is thespeed of the first canoe relative

to thewater? Answer in units of m/s.

(part 3 of3)

What is thespeed of the second canoe relative

to the water? Answer inunits of m/s.

Explanation / Answer

You are told in the beginning that they canoes have the samespeed relative to the water. So the answers to parts 2 and 3 arethe same, right? I'll call this v   the speed ofeach canoe relative to the water. .    Since the first canoe is paddled upstream, itsvelocity is    - v   (because downstreamis positive) relative to the water, and the second canoe hasvelocity   + v    relative to thewater. .    Of course the water moves in the positivedirection (downstream). I'll call the speed of thewater w. . Now the idea is that the velocity of each canoe relative tothe shore is simply the velocity of the canoe relative to thewater, PLUS the velocity of the water relative to shore. So we canwrite two equations: .     firstcanoe:       -1 = w - v .    second canoe:    2.2 = w + v . Then solve for w and v. Of course  w is the answer to part 1 and   v isthe answer to parts 2 and 3. You get: .          w = 0.6 m/s       (answer to part1)        v = 1.6m/s    (answer to parts 2 and 3)

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