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A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground?
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A body dropped from the top of a tower cover a distance 7x in the last...
Understanding the Problem
When a body is dropped from a height, it accelerates due to gravity. We know that the distance covered in the first second is 'x', and the distance covered in the last second of its journey is '7x'. Our goal is to determine the total time taken to reach the ground.
Key Formulas
- Distance covered in the first second:
- D1 = 1/2 * g * t^2
- Here, g = 9.8 m/s² (acceleration due to gravity), and t is the total time.
- Distance covered in the last second:
- D_last = (1/2 * g * t^2) - (1/2 * g * (t-1)^2)
- This can be simplified to:
D_last = g * t - 1/2 * g * (t-1)
Setting Up the Equation
From the problem, we know:
- D_last = 7x
- D1 = x
Substituting these into the distance equations gives:
7 * (1/2 * g * 1^2) = g * t - 1/2 * g * (t-1)^2
Simplifying this equation will lead us to the value of 't'.
Calculation Steps
1. Calculate D1:
D1 = 1/2 * g * 1^2 = 4.9 m
2. Calculate D_last:
D_last = 7x = 34.3 m
3. Using the equation from above, we can solve for t. After simplifying, we generally find that:
t = 4 seconds.
Conclusion
The total time taken to reach the ground is 4 seconds. This solution combines the principles of uniform acceleration and the specific conditions given in the problem. By understanding the relationships between the distances covered, we can derive the time taken for the body to fall.
When a body is dropped from a height, it accelerates due to gravity. We know that the distance covered in the first second is 'x', and the distance covered in the last second of its journey is '7x'. Our goal is to determine the total time taken to reach the ground.
Key Formulas
- Distance covered in the first second:
- D1 = 1/2 * g * t^2
- Here, g = 9.8 m/s² (acceleration due to gravity), and t is the total time.
- Distance covered in the last second:
- D_last = (1/2 * g * t^2) - (1/2 * g * (t-1)^2)
- This can be simplified to:
D_last = g * t - 1/2 * g * (t-1)
Setting Up the Equation
From the problem, we know:
- D_last = 7x
- D1 = x
Substituting these into the distance equations gives:
7 * (1/2 * g * 1^2) = g * t - 1/2 * g * (t-1)^2
Simplifying this equation will lead us to the value of 't'.
Calculation Steps
1. Calculate D1:
D1 = 1/2 * g * 1^2 = 4.9 m
2. Calculate D_last:
D_last = 7x = 34.3 m
3. Using the equation from above, we can solve for t. After simplifying, we generally find that:
t = 4 seconds.
Conclusion
The total time taken to reach the ground is 4 seconds. This solution combines the principles of uniform acceleration and the specific conditions given in the problem. By understanding the relationships between the distances covered, we can derive the time taken for the body to fall.
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A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground?
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A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground?.
A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body dropped from the top of a tower cover a distance 7x in the last second of it's journey , where x is the distance covered in first second. how mauch time dose it take to reach the ground?.
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