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A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index
of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an
instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-
of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an
instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-
- a)9 m/s
- b)12 m/s
- c)16 m/s
- d)21.33 m/s
Correct answer is option 'C'. Can you explain this answer?
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A ball is dropped from a height of 20 m above the surface of water in ...
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A ball is dropped from a height of 20 m above the surface of water in ...
Given:
- Height of the ball above the surface of water, h = 20 m
- Refractive index of water, n = 4/3
- Height of the ball above the water surface when the fish sees it, h' = 12.8 m
To find:
The speed of the ball when the fish sees it
Assumptions:
- The ball is dropped vertically downwards
- The fish is looking at the ball along the same line of fall
Concepts used:
- Snell's law of refraction: n₁sinθ₁ = n₂sinθ₂
- Speed of an object in a medium: v = √(gR), where g is the acceleration due to gravity and R is the distance fallen
Solution:
1. Let's assume the initial speed of the ball is u m/s and the final speed is v m/s.
2. Using the equation of motion, h = ut + (1/2)gt², we can find the time taken for the ball to fall from a height of 20 m:
- 20 = (1/2)gt² (since initial velocity u = 0)
- 40 = gt²
- t = √(40/g)
3. Similarly, let's find the time taken for the ball to fall from a height of 12.8 m:
- 12.8 = (1/2)gt²
- 25.6 = gt²
- t' = √(25.6/g)
4. Since the fish sees the ball at a height of 12.8 m, it means the light rays coming from the ball have been refracted by the water. Using Snell's law of refraction, we can find the angle of incidence, θ₁, and the angle of refraction, θ₂:
- n₁sinθ₁ = n₂sinθ₂
- sinθ₁ = (n₂/n₁)sinθ₂
- sinθ₁ = (4/3)sinθ₂
5. Since the fish is looking along the same line of fall, the angle of incidence, θ₁, is equal to the angle of elevation, θ:
- sinθ = sinθ₁ = (4/3)sinθ₂
6. Using the definition of sine, sinθ = opposite/hypotenuse, we can write:
- sinθ = (12.8/h') = (4/3)sinθ₂
7. Rearranging, we get sinθ₂ = (3/4)(12.8/h')
8. From the definition of sine, sinθ₂ = (v/u) = (v/0) = 0
9. Substituting the values in the equation, we get:
- 0 = (3/4)(12.8/h')
- h' = (3/4)(12.8) = 9.6
10. Since h' ≠ 12.8, our assumption that the final speed is v = 0 is incorrect.
11. Let's assume the final speed of the ball is v m/s.
12. Using the equation of motion, h' = ut' +
- Height of the ball above the surface of water, h = 20 m
- Refractive index of water, n = 4/3
- Height of the ball above the water surface when the fish sees it, h' = 12.8 m
To find:
The speed of the ball when the fish sees it
Assumptions:
- The ball is dropped vertically downwards
- The fish is looking at the ball along the same line of fall
Concepts used:
- Snell's law of refraction: n₁sinθ₁ = n₂sinθ₂
- Speed of an object in a medium: v = √(gR), where g is the acceleration due to gravity and R is the distance fallen
Solution:
1. Let's assume the initial speed of the ball is u m/s and the final speed is v m/s.
2. Using the equation of motion, h = ut + (1/2)gt², we can find the time taken for the ball to fall from a height of 20 m:
- 20 = (1/2)gt² (since initial velocity u = 0)
- 40 = gt²
- t = √(40/g)
3. Similarly, let's find the time taken for the ball to fall from a height of 12.8 m:
- 12.8 = (1/2)gt²
- 25.6 = gt²
- t' = √(25.6/g)
4. Since the fish sees the ball at a height of 12.8 m, it means the light rays coming from the ball have been refracted by the water. Using Snell's law of refraction, we can find the angle of incidence, θ₁, and the angle of refraction, θ₂:
- n₁sinθ₁ = n₂sinθ₂
- sinθ₁ = (n₂/n₁)sinθ₂
- sinθ₁ = (4/3)sinθ₂
5. Since the fish is looking along the same line of fall, the angle of incidence, θ₁, is equal to the angle of elevation, θ:
- sinθ = sinθ₁ = (4/3)sinθ₂
6. Using the definition of sine, sinθ = opposite/hypotenuse, we can write:
- sinθ = (12.8/h') = (4/3)sinθ₂
7. Rearranging, we get sinθ₂ = (3/4)(12.8/h')
8. From the definition of sine, sinθ₂ = (v/u) = (v/0) = 0
9. Substituting the values in the equation, we get:
- 0 = (3/4)(12.8/h')
- h' = (3/4)(12.8) = 9.6
10. Since h' ≠ 12.8, our assumption that the final speed is v = 0 is incorrect.
11. Let's assume the final speed of the ball is v m/s.
12. Using the equation of motion, h' = ut' +
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A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer?
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A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer?.
A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer?.
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A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive indexof water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At aninstant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as-a)9 m/sb)12 m/sc)16 m/sd)21.33 m/sCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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