A man can swim straight across a 100m wide river in 4 min if there is no current. If there is current it takes 5 min to cross straight. Determine the velocity of the current. Make a question like this but in a difficult way

### Problem:

A swimmer can cross a 200-meter-wide river in 6 minutes if there is no current. When there is a current, it takes him 9 minutes to cross straight across the river. Additionally, the swimmer swims at an angle of 30 degrees upstream relative to the riverbank to compensate for the current. Determine the velocity of the current.

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Do you need more details or have any questions? Here are 5 related questions:

1. How would the velocity of the swimmer relative to the riverbank change if the river width was doubled?
2. If the swimmer's speed was reduced by 20%, how long would it take him to cross the river without current?
3. What is the swimmer's velocity with respect to the ground in both cases (with and without current)?
4. How would the swimmer's trajectory change if he swam directly towards the opposite bank without compensating for the current?
5. If the current speed increased by 50%, how would the crossing time be affected?

**Tip:** When solving river problems, visualize the swimmer's motion as the resultant of two perpendicular vectors: the swimmer's velocity in still water and the river's current velocity.

A man can swim straight across a 100m wide river in 4 min if there is no current. If there is current it takes 5 min to cross straight. Determine the velocity of the current. Make a question like this but in a difficult way.

Explore a complex problem where a swimmer crosses a river with current, using relative velocity and vector analysis. This problem integrates concepts like the Pythagorean theorem and trigonometry, suitable for students in Grades 10-12. Detailed solution with formulas and visual explanation.

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