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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 −1.9 m/s and +2.8 m/s, respectively. What is the speed of each canoe relative to the water?

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Answer:

Speed of river is 0.45 m/s

Speed of boat is 2.65 m/s

Explanation:

[tex]v_r[/tex] = Speed of river

[tex]v_c[/tex] = Speed of canoe

[tex]v_r+v_c=2.8\ m/s[/tex]

[tex]v_r-v_c=-1.9\ m/s[/tex]

Adding the equations we get

[tex]2v_r=0.9\\\Rightarrow v_r=\frac{0.9}{2}\\\Rightarrow v_r=0.45\ m/s[/tex]

[tex]0.42+v_c=2.8\ m/s\\\Rightarrow v_c=2.8-0.45\\\Rightarrow v_c=2.65\ m/s[/tex]

Speed of river is 0.45 m/s

Speed of boat is 2.65 m/s

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