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A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim?
Most Upvoted Answer
A man can swim in still water with a speed of 2 m/s if he wants to cro...
If he want to swim through the shortest path then his resultant vector should be in perpendicular direction to the river flow. So, if x is the angle through which he has to swim against water flow then a right angled triangle is formed with root3 as perpendicular, shortest distance as base and 2 as hypotenuse. From trigonometry, sin x = root3/2 from which x = 60
Therefore, he must swim at an angle (90 + 60) = 150 degrees with the river flow.
Therefore, he must swim at an angle (90 + 60) = 150 degrees with the river flow.
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A man can swim in still water with a speed of 2 m/s if he wants to cro...
Solution
Introduction
When a man swims in a river, he will be affected by the water current. Thus, he must swim in a direction that will enable him to cross the river in the shortest possible distance.
Calculation
Given that the speed of the man is 2 m/s and the water current speed is √3 m/s. The angle at which the man should swim can be calculated using trigonometry.
Let θ be the angle at which the man should swim, then the horizontal component of his velocity will be 2 cosθ and the vertical component will be 2 sinθ. The water current will have a horizontal component of √3 and no vertical component.
The resultant velocity of the man and the water current will be the vector sum of their velocities. Since the man wants to cross the river in the shortest possible distance, he must swim perpendicular to the water current.
Thus, the horizontal component of the man's velocity should be equal and opposite to the horizontal component of the water current. Therefore, 2 cosθ = √3 and cosθ = √3/2. This implies that θ = 30°.
Conclusion
In conclusion, the man should swim at an angle of 30° to the direction of the water current. This will enable him to cross the river in the shortest possible distance.
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A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim?
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A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim?.
A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man can swim in still water with a speed of 2 m/s if he wants to cross the river of water current speed √3 M/s along the shortest path then in which direction should he swim?.
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