A boat is rowed directly upriver at a speed of 2.4 m/s relative to the water. Viewers on the shore see that the boat is moving at only 0.6 m/s relative to the shore (heading upriver). What is the speed of the river?
1.8 m/s
To find the speed of the river, we can subtract the speed of the boat relative to the shore from the speed of the boat relative to the water.
Speed of the boat relative to the shore = 0.6 m/s
Speed of the boat relative to the water = 2.4 m/s
Let's denote the speed of the river as "v".
Relative to the water, the boat is moving against the current of the river, so the effective speed of the boat relative to the water is the difference between the speed of the boat and the speed of the river.
2.4 m/s - v = 0.6 m/s
Now, let's solve for the speed of the river (v).
2.4 m/s - v = 0.6 m/s
Subtract 0.6 m/s from both sides of the equation:
2.4 m/s - 0.6 m/s = v
1.8 m/s = v
Therefore, the speed of the river is 1.8 m/s.
To find the speed of the river, we need to understand the concept of relative motion.
Let's assume the speed of the river is 'v' m/s, and the speed of the boat relative to the river (speed in still water) is 'b' m/s.
When the boat is moving upriver, it has to overcome the downstream current of the river. So, the effective speed of the boat relative to the river (upriver) is the difference between the boat's speed in still water and the speed of the river:
b - v
Since the boat is moving upriver at a speed of 0.6 m/s relative to the shore, we can say that the effective speed of the boat relative to the river is also 0.6 m/s:
b - v = 0.6
On the other hand, the boat's speed in still water is 2.4 m/s:
b = 2.4
Now we can substitute the value of 'b' from the second equation into the first equation:
2.4 - v = 0.6
To isolate 'v', we subtract 0.6 from both sides of the equation:
2.4 - 0.6 = v
v = 1.8
Therefore, the speed of the river is 1.8 m/s.