Two identical boats travel through still water at 3 m/s. They start from the same point, one travels parallel (and antiparallel) to the current and the other travels perpinducular. It takes one boat twice as long as the other. How fast is the current in the river flowing.
To find the speed of the current in the river, we can use the concept of relative velocity. Let's assume the speed of the current is represented by v (in meters per second).
For the boat traveling parallel (or antiparallel) to the current:
The boat's speed along with the current would be (3 + v) m/s.
The boat's speed against the current would be (3 - v) m/s.
For the boat traveling perpendicular to the current:
The boat's speed with respect to the current (which is perpendicular) is still 3 m/s.
Now, we are given that it takes one boat twice as long as the other. This means the time taken to travel a fixed distance is related to the speed inversely.
So, we can set up the following equation using the time (t) taken by the parallel boat and the time taken by the perpendicular boat:
(t for the parallel boat) = 2 * (t for the perpendicular boat)
To solve this, we need the distance traveled. However, since the distance is not given, we can assume a fixed distance (for example, 1 kilometer) for both boats.
The distance traveled by both boats will be the same since they start from the same point.
Using the formula: Distance = Speed * Time, we can write the equation for the distance traveled by both boats:
(3 + v) * t = 3 * (2t)
Simplifying the equation:
3t + vt = 6t
6t - 3t = vt
3t = vt
Dividing both sides by t:
3 = v
Therefore, the speed of the current in the river is 3 m/s.