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A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer?
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A stone dropped from the top of a tower is found to travel 5/9 of the ...
Explanation:
Let's assume the height of the tower is 'h' and time of fall is 't'.
Given, during the last second of its fall, the stone covers 5/9th of the height of the tower.
So, the distance covered in the last second = 5/9 * h
We know that the distance covered by a freely falling body in t seconds is given by the formula:
S = ut + (1/2)gt^2
Where, u = initial velocity = 0 m/s (as the stone is dropped)
g = acceleration due to gravity = 9.8 m/s^2 (downwards)
So, the distance covered by the stone in t seconds = h
Therefore, we can write the equation as:
h = 0 + (1/2)gt^2
=> t^2 = 2h/g
=> t = √(2h/g)
Now, we need to find the value of 't'.
So, let's substitute the given value of distance covered in the last second:
5/9h = u(1) + (1/2)g(1)^2
=> 5/9h = 0 + (1/2)g
=> (5/9)h = (1/2)g
Substituting the value of 'g' in terms of 'h':
(5/9)h = (1/2)(2h/t^2)
=> t^2 = (9/5) * 2
=> t = √(18/5) seconds
=> t = 3 seconds
Therefore, the time of fall is 3 seconds.
Let's assume the height of the tower is 'h' and time of fall is 't'.
Given, during the last second of its fall, the stone covers 5/9th of the height of the tower.
So, the distance covered in the last second = 5/9 * h
We know that the distance covered by a freely falling body in t seconds is given by the formula:
S = ut + (1/2)gt^2
Where, u = initial velocity = 0 m/s (as the stone is dropped)
g = acceleration due to gravity = 9.8 m/s^2 (downwards)
So, the distance covered by the stone in t seconds = h
Therefore, we can write the equation as:
h = 0 + (1/2)gt^2
=> t^2 = 2h/g
=> t = √(2h/g)
Now, we need to find the value of 't'.
So, let's substitute the given value of distance covered in the last second:
5/9h = u(1) + (1/2)g(1)^2
=> 5/9h = 0 + (1/2)g
=> (5/9)h = (1/2)g
Substituting the value of 'g' in terms of 'h':
(5/9)h = (1/2)(2h/t^2)
=> t^2 = (9/5) * 2
=> t = √(18/5) seconds
=> t = 3 seconds
Therefore, the time of fall is 3 seconds.
Community Answer
A stone dropped from the top of a tower is found to travel 5/9 of the ...
Let the stone travels for n second. according to question, distance in nth second =5/9 of height of tower so from the data, u+n^2*a/2= total height u+(2n-1) =5/9*total height as initially stone at rest, u=0 by dividing the equation and solving it, you get n=3 second
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A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer?
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A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer? 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 A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer?.
A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer? 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 A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone dropped from the top of a tower is found to travel 5/9 of the height of the tower during the last second of it's fall.The time of fall is. (1) 2s (2) 3s (3) 4s (4) 5s correct answer is option (2). can you explain this answer?.
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