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 shore?
(b) What is the speed of each canoe relative to the water?
canoe going upstream- m/s
canoe going downstream- m/s
vs+vb=2.9
vs-Vb=-1.2
solve for vs
solve for vb
both relative to water is vb-vs
To solve this problem, we can use the concept of relative velocities.
(a) The speed of the water relative to shore can be found by taking the average of the speeds of the two canoes. The average will give us the speed of the water relative to shore, regardless of the direction.
Speed of the water relative to shore = (Speed of the canoe going downstream + Speed of the canoe going upstream) / 2
Substituting the given values, we have:
Speed of the water relative to shore = (2.9 m/s + (-1.2 m/s)) / 2
= (2.9 - 1.2) / 2
= 1.7 / 2
= 0.85 m/s
Therefore, the speed of the water relative to shore is 0.85 m/s.
(b) The speed of each canoe relative to the water can be found by subtracting the speed of the water (found in part a) from the velocity of each canoe measured by the observer on shore. The velocities measured by the observer already include the speeds of the canoes relative to the water.
Speed of canoe going upstream = Velocity of canoe going upstream - Speed of the water relative to shore
Speed of canoe going upstream = -1.2 m/s - 0.85 m/s
= -2.05 m/s
Speed of canoe going downstream = Velocity of canoe going downstream - Speed of the water relative to shore
Speed of canoe going downstream = 2.9 m/s - 0.85 m/s
= 2.05 m/s
Therefore, the speed of the canoe going upstream is -2.05 m/s, and the speed of the canoe going downstream is 2.05 m/s.