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A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A particle is projected with a velocity v so that its range on a horiz...
Let the range be R and the maximum height be H. Given that R = 2H.
Range formula: R = (v2 sin 2θ) / g
Maximum height formula: H = (v2 sin2 θ) / (2g)
Given:
R = 2H
=> (v2 sin 2θ) / g = 2 × (v2 sin2 θ) / (2g)
=> sin 2θ = sin2 θ
Using sin 2θ = 2 sin θ cos θ, we get:
2 sin θ cos θ = sin2 θ
=> 2 cos θ = sin θ
=> tan θ = 2
Substitute tan θ = 2 to find sin 2θ:
sin 2θ = 2 sin θ cos θ
Using tan θ = 2, let sin θ = 2k and cos θ = k for some k.
Since sin2 θ + cos2 θ = 1:
(2k)2 + k2 = 1
4k2 + k2 = 1
5k2 = 1
k = 1/√5
So sin θ = 2/√5, cos θ = 1/√5.
sin 2θ = 2 × (2/√5) × (1/√5) = 4/5.
Therefore, range R = (v2 × 4/5) / g = 4v2 / 5g.
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A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. 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 A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. 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 A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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