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A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is?
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A swimmer A who wants to reach directly at point B on the other bank o...
**Solution:**
To find the time in which swimmer A crosses the river, we need to consider the velocity of the swimmer and the velocity of the river.
Let's break down the problem into its components:
1. **Given data:**
- Angle of swimming path = 37 degrees
- Width of the river = w
- Velocity of the river = Vo
2. **Components of swimmer's velocity:**
- The swimmer's velocity can be resolved into two components:
- Velocity perpendicular to the river flow (Vp)
- Velocity parallel to the river flow (Vr)
3. **Velocity perpendicular to the river flow (Vp):**
- Since the swimmer wants to reach directly to point B on the other bank, the perpendicular component of velocity should be zero.
- Therefore, Vp = 0
4. **Velocity parallel to the river flow (Vr):**
- The swimmer's velocity parallel to the river flow can be calculated using trigonometry.
- The component of the swimmer's velocity parallel to the river flow is given by Vr = V * cos(angle), where V is the magnitude of the swimmer's velocity.
5. **Net velocity of the swimmer:**
- The net velocity of the swimmer is the vector sum of Vp and Vr.
- Since Vp is zero, the net velocity of the swimmer is equal to Vr.
6. **Time taken to cross the river:**
- The time taken to cross the river is given by the formula: time = distance / velocity.
- In this case, the distance to be crossed is the width of the river, which is w.
- The velocity to be considered is the net velocity of the swimmer, which is Vr.
- Therefore, the time taken to cross the river is: time = w / Vr.
7. **Substituting values and solving:**
- We are given the angle of swimming path as 37 degrees.
- The velocity of the river is given as Vo.
- The magnitude of the swimmer's velocity can be determined as V = Vo / cos(angle).
- Substituting the values in the formula for time, we get: time = w / (Vo / cos(angle)).
- Simplifying the expression, we get: time = (w * cos(angle)) / Vo.
Hence, the time in which swimmer A crosses the river is given by (w * cos(37 degrees)) / Vo.
To find the time in which swimmer A crosses the river, we need to consider the velocity of the swimmer and the velocity of the river.
Let's break down the problem into its components:
1. **Given data:**
- Angle of swimming path = 37 degrees
- Width of the river = w
- Velocity of the river = Vo
2. **Components of swimmer's velocity:**
- The swimmer's velocity can be resolved into two components:
- Velocity perpendicular to the river flow (Vp)
- Velocity parallel to the river flow (Vr)
3. **Velocity perpendicular to the river flow (Vp):**
- Since the swimmer wants to reach directly to point B on the other bank, the perpendicular component of velocity should be zero.
- Therefore, Vp = 0
4. **Velocity parallel to the river flow (Vr):**
- The swimmer's velocity parallel to the river flow can be calculated using trigonometry.
- The component of the swimmer's velocity parallel to the river flow is given by Vr = V * cos(angle), where V is the magnitude of the swimmer's velocity.
5. **Net velocity of the swimmer:**
- The net velocity of the swimmer is the vector sum of Vp and Vr.
- Since Vp is zero, the net velocity of the swimmer is equal to Vr.
6. **Time taken to cross the river:**
- The time taken to cross the river is given by the formula: time = distance / velocity.
- In this case, the distance to be crossed is the width of the river, which is w.
- The velocity to be considered is the net velocity of the swimmer, which is Vr.
- Therefore, the time taken to cross the river is: time = w / Vr.
7. **Substituting values and solving:**
- We are given the angle of swimming path as 37 degrees.
- The velocity of the river is given as Vo.
- The magnitude of the swimmer's velocity can be determined as V = Vo / cos(angle).
- Substituting the values in the formula for time, we get: time = w / (Vo / cos(angle)).
- Simplifying the expression, we get: time = (w * cos(angle)) / Vo.
Hence, the time in which swimmer A crosses the river is given by (w * cos(37 degrees)) / Vo.
Community Answer
A swimmer A who wants to reach directly at point B on the other bank o...
Time - d /v sin theta
_AB/3v/5
5w/4/3v/5
_25w/12v
_AB/3v/5
5w/4/3v/5
_25w/12v
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A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is?
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A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is?.
A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A swimmer A who wants to reach directly at point B on the other bank of the river with angle 37degree swims with minimum possible speed with respect to river and reaches directly point B. If width of the river is w and river flows with velocity Vo ,then time in which swimmer crosses the river is?.
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