Asked Dec 17, 2019

Two canoeists in identical canoes exert the same effort
paddling and hence maintain the same speed relative to the
water. One paddles directly upstream (and moves upstream),
whereas the other paddles directly downstream. With downstream
as the positive direction, an observer on shore determines
the velocities of the two canoes to be -1.2 m/s and
+2.9 m/s, respectively. (a) What is the speed of the water relative
to the shore? (b) What is the speed of each canoe relative
to the water?


Expert Answer

Step 1



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Taking downstream as the positive direction, the velocity of the water relative to the shore is vws = vws vws is the speed of the flowing water If the common speed of the water is vcw, Here, (vcw)downstream (vcw)upstream UCW -vCW vcw is the velocity of the canoe with respect to the water

Step 2



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The velocity of the canoe moving downstream relative to the water is, VCW = VCS – vws Substitute 2.9 m/s for vcs. VCw =2.9m/s – vws (1) The velocity of the canoe moving upstream relative to the water is, -vCW = UCS UwS Substitute –1.2 m/s for vcs. -vCw = -1.2m/s – vws (2) Adding equations (I) and (II), 2vws = 1.7 m/s vws = 0.85 m/s The speed of the water relative to the shore is 0.85 m/s.


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