Two paddlers in identical canoes exert the same effort paddling and hence mainta

Question

Two paddlers 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. If downstream is 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 velocity of the water relative to shore?

(b) What is the velocity of each canoe relative to the water?
(canoe going upstream),
(canoe going downstream)

Explanation / Answer

(a) W : water D : downstream boat U : upstream boat G : ground or shore or man V(W G ) means velocity of water with respect to the ground , this is the notation that i will follow. V(U G) = - 1.2 V ( D G) = + 2.9 V( W G ) = ? we know that V(1 3 ) = V( 1 2 ) + V ( 2 3) we also know that the speed of boats with respect to water are the same. so V ( U W) = - V ( D W ) V ( U G ) + V( G W ) = - [ V ( D G ) + V ( G W ) ] implies V( U G ) + V ( D G ) = - 2 * V ( G W ) implies -1.2 + 2.9 = - 2 * V ( G W ) implies V (G W ) = -0 .85 or V ( W G ) = + 0.85 m/s

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