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From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?
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Problem:
From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P, its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?
Solution:
Let's assume that the initial velocity of the stone is u and it reaches a maximum height of h1 before starting to fall back down. The velocity of the stone at height h above P can be calculated using the formula:
v1^2 = u^2 - 2gh
where g is the acceleration due to gravity.
When the stone reaches a distance h below P, its velocity can be calculated using the same formula:
v2^2 = u^2 + 2gh
Since we know that the velocity at h is double of the velocity at h1, we can write:
2v1^2 = v2^2
Substituting the values of v1^2 and v2^2 in the above equation, we get:
2(u^2 - 2gh)^2 = (u^2 + 2gh)^2
Simplifying the above equation, we get:
h = u^2/8g
This means that the maximum height attained by the stone is directly proportional to the square of the initial velocity and inversely proportional to the acceleration due to gravity.
Therefore, the greatest height attained by the stone from the point of projection P is h1 + h, which is equal to:
h1 + u^2/8g
Conclusion:
The maximum height attained by the stone can be calculated using the formula h1 + u^2/8g, where h1 is the maximum height reached before starting to fall back down, u is the initial velocity of the stone and g is the acceleration due to gravity.
From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P, its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?
Solution:
Let's assume that the initial velocity of the stone is u and it reaches a maximum height of h1 before starting to fall back down. The velocity of the stone at height h above P can be calculated using the formula:
v1^2 = u^2 - 2gh
where g is the acceleration due to gravity.
When the stone reaches a distance h below P, its velocity can be calculated using the same formula:
v2^2 = u^2 + 2gh
Since we know that the velocity at h is double of the velocity at h1, we can write:
2v1^2 = v2^2
Substituting the values of v1^2 and v2^2 in the above equation, we get:
2(u^2 - 2gh)^2 = (u^2 + 2gh)^2
Simplifying the above equation, we get:
h = u^2/8g
This means that the maximum height attained by the stone is directly proportional to the square of the initial velocity and inversely proportional to the acceleration due to gravity.
Therefore, the greatest height attained by the stone from the point of projection P is h1 + h, which is equal to:
h1 + u^2/8g
Conclusion:
The maximum height attained by the stone can be calculated using the formula h1 + u^2/8g, where h1 is the maximum height reached before starting to fall back down, u is the initial velocity of the stone and g is the acceleration due to gravity.
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From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?
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From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?.
From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From an elevated point P, a stone is projected vertically upwards. When the stone reaches a distance h below P.,its velocity is double of its velocity at a height h above P. The greatest height attained by the stone from the point of projection P is?.
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