Final answer:
The rate of flow of the river is 2 m/s. The swimmer counteracts the river's flow rate by swimming with a cross-river component of 2 m/s, which is half of their swimming speed due to the 120° angle.
Step-by-step explanation:
To solve for the rate of flow of the river, we need to understand vector components and use trigonometry to find the resultant velocities.
The swimmer's velocity making a 120° angle with the direction of flow is equivalent to heading upstream at an angle of 60° from directly across the river, considering the flow of the river itself.
We'll decompose the swimmer's velocity into two components: one perpendicular to the river's flow (the cross-river component) and the other parallel to the river's flow (the upstream component).
We can use the cosine function to find the cross-river component due to the 60° angle (cos(60°) = 0.5).
Multiplying the swimmer's speed by this cosine value gives us the cross-river speed: 4 m/s * 0.5 = 2 m/s.
Since the question assumes the swimmer is able to reach the directly opposite point, they must exactly counteract the river's flow.
Thus, the rate of flow of the river must be 2 m/s, which is choice (A).
By the upstream component, we know that the swimmer's speed must be adding to the river's speed to equal the 4 m/s swimming speed, but since the cross-river component alone is 2 m/s, and he reaches the opposite point directly, the river's rate of flow cannot be more than 2 m/s.