NEET Exam > NEET Questions > The speed of boat is 5 km/h in still water. I...
Start Learning for Free
The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water is
- a)1 km/h
- b)3 km/h
- c)4 km/h
- d)5 km/h
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The speed of boat is 5 km/h in still water. It crosses a river of widt...
Shortest path is along line AB.
If the boat crosses the river in 15 min
⇒
= 4 km/hr ∴ 
= 3 km/hrFree Test
FREE
| Start Free Test |
Community Answer
The speed of boat is 5 km/h in still water. It crosses a river of widt...
Understanding the Problem
To determine the velocity of the river water, we need to analyze the boat's movement across the river.
Key Given Information
- Speed of the boat in still water: 5 km/h
- Width of the river: 1 km
- Time taken to cross the river: 15 minutes (which is 0.25 hours)
Calculating the Boat's Effective Speed
1. Distance Traveled:
- The boat crosses a width of 1 km.
2. Effective Speed:
- The effective speed required to cross 1 km in 15 minutes (0.25 hours) is:
- Speed = Distance / Time = 1 km / 0.25 h = 4 km/h.
Analyzing the Velocity Components
To cross the river optimally, the boat's velocity has two components:
- Velocity across the river (perpendicular to the current): This is the effective speed calculated as 4 km/h.
- Velocity downstream (due to the current): This is the unknown we need to find.
Using Pythagorean Theorem
When the boat crosses the river, the boat's speed in still water and the river's speed create a right triangle:
- Speed of the boat: 5 km/h (hypotenuse)
- Effective speed across the river: 4 km/h (one side)
- Velocity of river water (current): x (other side)
Using the Pythagorean theorem:
(5 km/h)² = (4 km/h)² + (x)²
Solving gives:
25 = 16 + x²
x² = 9
x = 3 km/h
Conclusion
The velocity of the river water is 3 km/h, confirming the correct answer is option 'B'.
To determine the velocity of the river water, we need to analyze the boat's movement across the river.
Key Given Information
- Speed of the boat in still water: 5 km/h
- Width of the river: 1 km
- Time taken to cross the river: 15 minutes (which is 0.25 hours)
Calculating the Boat's Effective Speed
1. Distance Traveled:
- The boat crosses a width of 1 km.
2. Effective Speed:
- The effective speed required to cross 1 km in 15 minutes (0.25 hours) is:
- Speed = Distance / Time = 1 km / 0.25 h = 4 km/h.
Analyzing the Velocity Components
To cross the river optimally, the boat's velocity has two components:
- Velocity across the river (perpendicular to the current): This is the effective speed calculated as 4 km/h.
- Velocity downstream (due to the current): This is the unknown we need to find.
Using Pythagorean Theorem
When the boat crosses the river, the boat's speed in still water and the river's speed create a right triangle:
- Speed of the boat: 5 km/h (hypotenuse)
- Effective speed across the river: 4 km/h (one side)
- Velocity of river water (current): x (other side)
Using the Pythagorean theorem:
(5 km/h)² = (4 km/h)² + (x)²
Solving gives:
25 = 16 + x²
x² = 9
x = 3 km/h
Conclusion
The velocity of the river water is 3 km/h, confirming the correct answer is option 'B'.
|
Explore Courses for NEET exam
|
|
Top Courses for NEETView all
Question Description
The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer?.
The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along shortest possible path in 15 min. The velocity of river water isa)1 km/hb)3 km/hc)4 km/hd)5 km/hCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily