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 in m/s?
(b) What is the speed of each canoe relative to the water?
canoe going upstream- m/s
canoe going downstream- m/s
To answer this question, we need to use the concept of relative velocity and apply it to the given scenario. Relative velocity is the velocity of an object as observed from another object or reference frame.
(a) To find the speed of the water relative to the shore, we need to consider the velocity of the canoe going upstream and downstream. Since the canoe going upstream has a velocity of -1.2 m/s relative to the shore and the canoe going downstream has a velocity of +2.9 m/s relative to the shore, we can deduce that the current is faster than the canoe going upstream and slower than the canoe going downstream.
Let's assume the speed of the water relative to the shore is v. So, the velocity of the canoe going upstream relative to the water will be v - 1.2 m/s, and the velocity of the canoe going downstream relative to the water will be v + 2.9 m/s.
Since the two canoes exert the same effort paddling and maintain the same speed relative to the water, we can equate their relative velocities to water as:
v - 1.2 m/s = v + 2.9 m/s
Solving this equation, we find:
-1.2 m/s = 2.9 m/s
v = 2.9 m/s - (-1.2 m/s)
v = 4.1 m/s
Therefore, the speed of the water relative to the shore is 4.1 m/s.
(b) To find the speed of each canoe relative to the water, we can now substitute the value of v we just calculated into the equations:
- The canoe going upstream has a velocity of v - 1.2 m/s. Substituting v = 4.1 m/s, we get:
Canoe going upstream speed = 4.1 m/s - 1.2 m/s = 2.9 m/s.
- The canoe going downstream has a velocity of v + 2.9 m/s. Substituting v = 4.1 m/s, we get:
Canoe going downstream speed = 4.1 m/s + 2.9 m/s = 7.0 m/s.
Therefore, the speed of the canoe going upstream relative to the water is 2.9 m/s, and the speed of the canoe going downstream relative to the water is 7.0 m/s.