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A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution?
Most Upvoted Answer
A stone falls freely from rest from a height h and it travels a distan...
C
Distance travelled in (t-1) time=
h -(9h/25)=16h/25
now 16h/25 = 0+[(1/2)g(t-1)²] _________(1)
also , h=0+(1/2)gt² _________(2)
Solving these equations,we get
t=5
so h=(1/2)gt²=122.5 m
Take g=9.8
Distance travelled in (t-1) time=
h -(9h/25)=16h/25
now 16h/25 = 0+[(1/2)g(t-1)²] _________(1)
also , h=0+(1/2)gt² _________(2)
Solving these equations,we get
t=5
so h=(1/2)gt²=122.5 m
Take g=9.8
Community Answer
A stone falls freely from rest from a height h and it travels a distan...
Solution:
Given,
Distance travelled by stone in the last second = 9h/25
Let's consider the time taken by the stone to travel the distance of 9h/25 in the last second as t.
So, we can say that the stone has covered the remaining distance (h - 9h/25) in (t - 1) seconds.
Using the formula for distance travelled by an object under free fall, we get
h - 9h/25 = (1/2) * g * (t - 1)^2 --- (1)
where g is acceleration due to gravity.
Now, let's consider the distance travelled by the stone in the last second.
Using the formula for distance travelled by an object under constant acceleration, we get
9h/25 = (1/2) * g * t^2 --- (2)
Dividing equation (2) by equation (1), we get
(9h/25) / (h - 9h/25) = t^2 / ((t - 1)^2)
Simplifying the above equation, we get
t^2 - (18/25)t + 1 = 0
On solving the above quadratic equation, we get
t = 1 second or t = 1/25 second (which is not possible as it implies negative time)
Therefore, the time taken by the stone to travel the distance of 9h/25 in the last second is 1 second.
Using equation (2), we can find the value of h as follows:
9h/25 = (1/2) * g * t^2
9h/25 = (1/2) * 9.8 * 1^2 (as g = 9.8 m/s^2)
h = 49/4 = 12.25 m
Therefore, the height from which the stone falls is h = 12.25 m.
Hence, the correct option is (c) 122.5m.
Given,
Distance travelled by stone in the last second = 9h/25
Let's consider the time taken by the stone to travel the distance of 9h/25 in the last second as t.
So, we can say that the stone has covered the remaining distance (h - 9h/25) in (t - 1) seconds.
Using the formula for distance travelled by an object under free fall, we get
h - 9h/25 = (1/2) * g * (t - 1)^2 --- (1)
where g is acceleration due to gravity.
Now, let's consider the distance travelled by the stone in the last second.
Using the formula for distance travelled by an object under constant acceleration, we get
9h/25 = (1/2) * g * t^2 --- (2)
Dividing equation (2) by equation (1), we get
(9h/25) / (h - 9h/25) = t^2 / ((t - 1)^2)
Simplifying the above equation, we get
t^2 - (18/25)t + 1 = 0
On solving the above quadratic equation, we get
t = 1 second or t = 1/25 second (which is not possible as it implies negative time)
Therefore, the time taken by the stone to travel the distance of 9h/25 in the last second is 1 second.
Using equation (2), we can find the value of h as follows:
9h/25 = (1/2) * g * t^2
9h/25 = (1/2) * 9.8 * 1^2 (as g = 9.8 m/s^2)
h = 49/4 = 12.25 m
Therefore, the height from which the stone falls is h = 12.25 m.
Hence, the correct option is (c) 122.5m.
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A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution?
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A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution?.
A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone falls freely from rest from a height h and it travels a distance 9h/25 in last second. Then h is a. 145m b. 100m c. 122.5m d. 200m e. 175m. plz explain the solution?.
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