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The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.
If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given by
- a)45∘ west
- b)30∘ west
- c)0∘
- d)60∘ west
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The speed of a swimmer in still water is 20m∕s. The speed of river wa...
Given:
- Speed of swimmer in still water = 20 m/s
- Speed of river water = 10 m/s (flowing due east)
To find:
The angle at which the swimmer should make his strokes with respect to the north.
Solution:
To cross the river along the shortest path, the swimmer needs to consider the effect of the river's flow on his motion.
Step 1: Analyzing the situation
- Let's assume that the swimmer is moving towards the north direction.
- The swimmer's speed in the north direction (Vn) can be calculated using the Pythagorean theorem:
Vn² = (20 m/s)² - (10 m/s)²
= 400 m²/s² - 100 m²/s²
= 300 m²/s²
Vn = √300 m/s ≈ 17.32 m/s
- The river's speed is towards the east, so it will not affect the swimmer's northward velocity.
Step 2: Calculating the angle
- The angle at which the swimmer should make his strokes with respect to the north can be calculated using trigonometry.
- Let θ be the angle.
- The tangent of θ is given by the ratio of the river's speed (10 m/s) to the swimmer's northward speed (17.32 m/s).
- Tan(θ) = 10 m/s / 17.32 m/s
- θ = arctan(10/17.32)
- Using a calculator, θ ≈ 30°
Therefore, the angle at which the swimmer should make his strokes with respect to the north is approximately 30° west (option B).
- Speed of swimmer in still water = 20 m/s
- Speed of river water = 10 m/s (flowing due east)
To find:
The angle at which the swimmer should make his strokes with respect to the north.
Solution:
To cross the river along the shortest path, the swimmer needs to consider the effect of the river's flow on his motion.
Step 1: Analyzing the situation
- Let's assume that the swimmer is moving towards the north direction.
- The swimmer's speed in the north direction (Vn) can be calculated using the Pythagorean theorem:
Vn² = (20 m/s)² - (10 m/s)²
= 400 m²/s² - 100 m²/s²
= 300 m²/s²
Vn = √300 m/s ≈ 17.32 m/s
- The river's speed is towards the east, so it will not affect the swimmer's northward velocity.
Step 2: Calculating the angle
- The angle at which the swimmer should make his strokes with respect to the north can be calculated using trigonometry.
- Let θ be the angle.
- The tangent of θ is given by the ratio of the river's speed (10 m/s) to the swimmer's northward speed (17.32 m/s).
- Tan(θ) = 10 m/s / 17.32 m/s
- θ = arctan(10/17.32)
- Using a calculator, θ ≈ 30°
Therefore, the angle at which the swimmer should make his strokes with respect to the north is approximately 30° west (option B).
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Community Answer
The speed of a swimmer in still water is 20m∕s. The speed of river wa...
⇒ θ = 180∘ − (90∘ + 60∘) = 30∘
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The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. Can you explain this answer?
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The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. 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 speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. 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 speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. Can you explain this answer?.
The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. 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 speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. 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 speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given bya)45∘ westb)30∘ westc)0∘d)60∘ westCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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