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
To find the answers, let's break down the given information and solve the problem step by step.
(a) What is the speed of the water relative to the shore?
The speed of the water relative to the shore can be calculated by taking the average of the speeds of the canoe going upstream and the canoe going downstream.
Given:
Velocity of the canoe going upstream (relative to the shore) = -1.2 m/s
Velocity of the canoe going downstream (relative to the shore) = +2.9 m/s
To find the speed of the water relative to the shore, we can use the formula:
Speed of water (relative to shore) = (Velocity downstream + Velocity upstream) / 2
Plugging in the values, we get:
Speed of water (relative to shore) = (2.9 m/s + -1.2 m/s) / 2
= 1.7 m/s / 2
= 0.85 m/s
Therefore, the speed of the water relative to the shore is 0.85 m/s.
(b) What is the speed of each canoe relative to the water?
The speed of each canoe relative to the water can be found by subtracting the speed of the water (from part a) from their respective velocities relative to the shore.
Given:
Velocity of the canoe going upstream (relative to the shore) = -1.2 m/s
Velocity of the canoe going downstream (relative to the shore) = +2.9 m/s
Speed of water (relative to the shore) = 0.85 m/s
Speed of canoe going upstream (relative to water) = Velocity of the canoe going upstream - Speed of water
= -1.2 m/s - 0.85 m/s
= -2.05 m/s
Speed of canoe going downstream (relative to water) = Velocity of the canoe going downstream - Speed of water
= 2.9 m/s - 0.85 m/s
= 2.05 m/s
Therefore,
Speed of canoe going upstream (relative to water) = -2.05 m/s
Speed of canoe going downstream (relative to water) = 2.05 m/s
So, the canoe going upstream has a speed of -2.05 m/s relative to the water, while the canoe going downstream has a speed of 2.05 m/s relative to the water.
a. 2.05
b. 0.85