Class 10 Exam > Class 10 Questions > An object is thrown upwards with an initial v...
Start Learning for Free
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?
Verified Answer
An object is thrown upwards with an initial velocity of 17m/sec from a...
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
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).
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup