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An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground?
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An object is thrown upwards with an initial velocity of 17m/sec from a...
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An object is thrown upwards with an initial velocity of 17m/sec from a...
Analysis:
To solve this problem, we can use the kinematic equation that relates the vertical displacement, initial velocity, time, and acceleration.
The equation is given by:
S = ut + (1/2)at^2
Where:
- S is the vertical displacement (height)
- u is the initial velocity
- t is the time
- a is the acceleration (in this case, the acceleration due to gravity, which is approximately -9.8 m/s^2)
Given:
- Initial velocity (u) = 17 m/s
- Height (S) = 12 m
Calculating the time taken to touch the ground:
We can substitute the values into the equation and solve for time.
12 = 17t - (1/2)(9.8)t^2
Simplifying the equation:
12 = 17t - 4.9t^2
Rearranging the equation to form a quadratic equation:
4.9t^2 - 17t + 12 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 4.9, b = -17, and c = 12.
Substituting the values into the formula:
t = (17 ± √((-17)^2 - 4(4.9)(12))) / (2(4.9))
Simplifying the equation further:
t = (17 ± √(289 - 235.2)) / 9.8
t = (17 ± √53.8) / 9.8
Calculating the square root of 53.8:
t ≈ (17 ± 7.34) / 9.8
This gives us two possible solutions:
t ≈ (17 + 7.34) / 9.8 ≈ 2.5 seconds
t ≈ (17 - 7.34) / 9.8 ≈ 0.97 seconds
Conclusion:
The time taken by the object to touch the ground is approximately 2.5 seconds or 0.97 seconds, depending on the direction of time (upwards or downwards).
To solve this problem, we can use the kinematic equation that relates the vertical displacement, initial velocity, time, and acceleration.
The equation is given by:
S = ut + (1/2)at^2
Where:
- S is the vertical displacement (height)
- u is the initial velocity
- t is the time
- a is the acceleration (in this case, the acceleration due to gravity, which is approximately -9.8 m/s^2)
Given:
- Initial velocity (u) = 17 m/s
- Height (S) = 12 m
Calculating the time taken to touch the ground:
We can substitute the values into the equation and solve for time.
12 = 17t - (1/2)(9.8)t^2
Simplifying the equation:
12 = 17t - 4.9t^2
Rearranging the equation to form a quadratic equation:
4.9t^2 - 17t + 12 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 4.9, b = -17, and c = 12.
Substituting the values into the formula:
t = (17 ± √((-17)^2 - 4(4.9)(12))) / (2(4.9))
Simplifying the equation further:
t = (17 ± √(289 - 235.2)) / 9.8
t = (17 ± √53.8) / 9.8
Calculating the square root of 53.8:
t ≈ (17 ± 7.34) / 9.8
This gives us two possible solutions:
t ≈ (17 + 7.34) / 9.8 ≈ 2.5 seconds
t ≈ (17 - 7.34) / 9.8 ≈ 0.97 seconds
Conclusion:
The time taken by the object to touch the ground is approximately 2.5 seconds or 0.97 seconds, depending on the direction of time (upwards or downwards).
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An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground?
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An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground?.
An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is thrown upwards with an initial velocity of 17m/sec from a building with 12 m height it is at a height of S=12 17t-5t^from the ground after a flight of t seconds find the time taken by the object to touch the ground?.
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