A river flows with a speed more than the maximum speed with which a person can swim in still water. He intends to cross the river by the shortest possible path (i.e., he wants to reach the point on the opposite bank which directly opposite to the starting point). Which of the following is correct ?

Options

A. He should normal to the river bank.
B. He should start in such a way that he moves normal to the bank, relative to the bank.
C. He should start in a particular (calculated) direction making an obtuse angle with the direction of water current.
D. The man cannot cross the river in that way.

Explanation

To solve the problem of a person trying to cross a river that flows faster than he can swim, we need to analyze the situation step by step.

### Step 1: Understand the scenario
The river flows with a speed greater than the maximum speed at which the person can swim in still water. This means that if the person swims directly across the river, he will be swept downstream by the current.

**Hint:** Visualize the river and the swimmer's movement. Draw a diagram to represent the river's current and the swimmer's intended path.

### Step 2: Define the goal
The person wants to reach a point directly opposite his starting point on the opposite bank. This means he needs to compensate for the river's current while swimming.

**Hint:** Consider the concept of relative motion. The swimmer's velocity relative to the riverbank is the vector sum of his swimming velocity and the river's current.

### Step 3: Determine the direction of swimming
To reach the opposite bank directly across from the starting point, the swimmer must swim at an angle upstream. This angle will allow him to counteract the downstream flow of the river.

**Hint:** Think about the triangle formed by the swimmer's velocity, the river's current, and the resultant velocity that points directly across the river.

### Step 4: Analyze the swimmer's velocity
Let’s denote:
- \( v_s \): the swimmer's speed in still water (which is less than the river's speed).
- \( v_r \): the speed of the river current.

To reach the opposite bank directly, the swimmer must swim at an angle θ such that the component of his swimming velocity against the current equals the current's speed.

**Hint:** Use trigonometric relationships to find the angle θ. The swimmer's velocity can be broken down into two components: one against the current and one across the river.

### Step 5: Conclusion
The swimmer must aim upstream at an angle to ensure that his resultant path is perpendicular to the banks of the river. This way, he can reach the point directly opposite his starting position.

Thus, the correct answer is that the swimmer should start in such a way that he moves normal to the bank relative to the bank.

**Final Answer:** The correct option is that the swimmer should swim at an angle upstream to reach the point directly opposite his starting point.

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