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The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river in
- a)3.6 min
- b)8 min
- c)3 min
- d)5 min
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The width of a river is 25 m and water is flowing in it with a speed o...
Given:
- Width of the river = 25m
- Speed of water current = 4m/min
- Speed of boat relative to water = 8m/min
To find:
- Time taken by the boatman to cross the river
Approach:
- We can use the concept of relative velocity to solve this problem
- Let's assume the boatman sails in a straight line from his position to the opposite bank of the river
- We can break down the boat's velocity into two components - one along the direction of the water current and the other perpendicular to it
- The component along the water current will help the boatman maintain his position with respect to the bank
- The perpendicular component will help the boatman cross the river
- We can calculate the time taken for the boatman to cross the river using the distance to be covered and the perpendicular component of velocity
Calculation:
- Let's first calculate the perpendicular component of velocity
- We can use Pythagoras theorem to calculate the hypotenuse of the right triangle formed by the boat's velocity and the water current velocity
- Hypotenuse = √(8^2 + 4^2) = √(64+16) = √80 m/min
- The perpendicular component of velocity will be equal to the length of the side of the triangle opposite to the angle between the boat's velocity and the perpendicular
- This angle can be calculated using trigonometry as tanθ = perpendicular/hypotenuse = 4/8 = 0.5
- θ = tan^-1(0.5) = 26.56 degrees
- The perpendicular component of velocity = hypotenuse * sin(θ) = √80 * sin(26.56) = 22.63 m/min
- Now, we can calculate the time taken by the boatman to cross the river using the formula:
- Time = distance/velocity
- Distance to be covered = width of the river = 25m
- Velocity = perpendicular component of velocity = 22.63 m/min
- Time taken = 25/22.63 = 1.105 min
- However, this time represents the time taken by the boatman in still water
- Since the water current is flowing, the boatman will also be carried downstream while crossing the river
- The downstream distance covered by the boatman will be equal to the product of the water current speed and the time taken to cross the river
- Downstream distance = 4 * 1.105 = 4.42 m
- This means that the boatman will actually end up at a point downstream from the opposite bank of the river
- To calculate the actual time taken to reach the opposite bank, we need to use the concept of relative velocity again
- The boatman will need to cover the remaining distance to the opposite bank, which is equal to the perpendicular distance from his landing point to the opposite bank
- Let's assume this distance is x meters
- The time taken to cover this distance will be x/8 min
- The boatman will also be carried downstream by the water current during this time
- The downstream distance covered will be equal to the product of the water current speed and the time taken to cover the remaining distance
- Downstream distance = 4 * x/8 = x/2 m
- Width of the river = 25m
- Speed of water current = 4m/min
- Speed of boat relative to water = 8m/min
To find:
- Time taken by the boatman to cross the river
Approach:
- We can use the concept of relative velocity to solve this problem
- Let's assume the boatman sails in a straight line from his position to the opposite bank of the river
- We can break down the boat's velocity into two components - one along the direction of the water current and the other perpendicular to it
- The component along the water current will help the boatman maintain his position with respect to the bank
- The perpendicular component will help the boatman cross the river
- We can calculate the time taken for the boatman to cross the river using the distance to be covered and the perpendicular component of velocity
Calculation:
- Let's first calculate the perpendicular component of velocity
- We can use Pythagoras theorem to calculate the hypotenuse of the right triangle formed by the boat's velocity and the water current velocity
- Hypotenuse = √(8^2 + 4^2) = √(64+16) = √80 m/min
- The perpendicular component of velocity will be equal to the length of the side of the triangle opposite to the angle between the boat's velocity and the perpendicular
- This angle can be calculated using trigonometry as tanθ = perpendicular/hypotenuse = 4/8 = 0.5
- θ = tan^-1(0.5) = 26.56 degrees
- The perpendicular component of velocity = hypotenuse * sin(θ) = √80 * sin(26.56) = 22.63 m/min
- Now, we can calculate the time taken by the boatman to cross the river using the formula:
- Time = distance/velocity
- Distance to be covered = width of the river = 25m
- Velocity = perpendicular component of velocity = 22.63 m/min
- Time taken = 25/22.63 = 1.105 min
- However, this time represents the time taken by the boatman in still water
- Since the water current is flowing, the boatman will also be carried downstream while crossing the river
- The downstream distance covered by the boatman will be equal to the product of the water current speed and the time taken to cross the river
- Downstream distance = 4 * 1.105 = 4.42 m
- This means that the boatman will actually end up at a point downstream from the opposite bank of the river
- To calculate the actual time taken to reach the opposite bank, we need to use the concept of relative velocity again
- The boatman will need to cover the remaining distance to the opposite bank, which is equal to the perpendicular distance from his landing point to the opposite bank
- Let's assume this distance is x meters
- The time taken to cover this distance will be x/8 min
- The boatman will also be carried downstream by the water current during this time
- The downstream distance covered will be equal to the product of the water current speed and the time taken to cover the remaining distance
- Downstream distance = 4 * x/8 = x/2 m
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The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer?
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The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer?.
The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice The width of a river is 25 m and water is flowing in it with a speed of 4m/min. A boatman is standing on the bank of the river. He wants to sail the boat to a point on the other bank directly opposite to him. He can sail the boat at 8 m/min relative to water. He will cross the river ina)3.6 minb)8 minc)3 mind)5 minCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice NEET tests.
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