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A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone is
a. 8 m s−1
b. 15 m s−1
c. 12 m s−1
d. 9 m s−1?
a. 8 m s−1
b. 15 m s−1
c. 12 m s−1
d. 9 m s−1?
Most Upvoted Answer
A stone is projected from a point on the ground in such a way so as to...
Given:
- Initial height of the bird, h = 3h
- Maximum height of the stone, 4h
- Horizontal speed of the bird, 10 m/s
Calculating Time of Flight:
- Let the initial speed of the stone be u m/s.
- At maximum height, vertical component of velocity = 0
- Using the equation v^2 = u^2 + 2as, where v = 0, a = -g and s = 4h,
we get 0 = u^2 - 8gh
- Solving for u, we get u = √(8gh)
- Time taken to reach maximum height, t = u/g
- Total time of flight = 2t
Calculating Horizontal Range:
- Horizontal range, R = Horizontal speed * Total time of flight
- R = 10 * 2t = 20t
Calculating Horizontal Distance Covered by Bird:
- Horizontal distance covered by bird in time t = 10t
- Horizontal distance covered by bird = 10t
Since the stone hits the bird, the horizontal range and the horizontal distance covered by the bird must be equal:
- 20t = 10t
- t = 0.5 seconds
Calculating Horizontal Velocity of Stone:
- Horizontal velocity of stone = Horizontal range / Total time of flight
- Horizontal velocity of stone = 20t / 2t = 10 m/s
Therefore, the horizontal velocity of the stone is 10 m/s. This means option b. 15 m/s, is incorrect.
- Initial height of the bird, h = 3h
- Maximum height of the stone, 4h
- Horizontal speed of the bird, 10 m/s
Calculating Time of Flight:
- Let the initial speed of the stone be u m/s.
- At maximum height, vertical component of velocity = 0
- Using the equation v^2 = u^2 + 2as, where v = 0, a = -g and s = 4h,
we get 0 = u^2 - 8gh
- Solving for u, we get u = √(8gh)
- Time taken to reach maximum height, t = u/g
- Total time of flight = 2t
Calculating Horizontal Range:
- Horizontal range, R = Horizontal speed * Total time of flight
- R = 10 * 2t = 20t
Calculating Horizontal Distance Covered by Bird:
- Horizontal distance covered by bird in time t = 10t
- Horizontal distance covered by bird = 10t
Since the stone hits the bird, the horizontal range and the horizontal distance covered by the bird must be equal:
- 20t = 10t
- t = 0.5 seconds
Calculating Horizontal Velocity of Stone:
- Horizontal velocity of stone = Horizontal range / Total time of flight
- Horizontal velocity of stone = 20t / 2t = 10 m/s
Therefore, the horizontal velocity of the stone is 10 m/s. This means option b. 15 m/s, is incorrect.
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A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1?
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A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1?.
A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1?.
Solutions for A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s−1 and the stone still hits the bird while descending, then the horizontal velocity of stone isa. 8 m s−1b. 15 m s−1c. 12 m s−1d. 9 m s−1? in English & in Hindi are available as part of our courses for UPSC.
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