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A stone falls freely from rest from a height h and it travels a distance of 9h/25 in the last second. The value of h is: (Take g = 10 m/s2):
- a)145 m
- b)100 m
- c)125 m
- d)200 ms
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A stone falls freely from rest from a height h and it travels a distan...
Understanding the problem
The problem states that a stone falls freely from a height 'h' and it travels a distance of 9h/25 in the last second. We are given the value of acceleration due to gravity as 10 m/s^2. We need to find the value of 'h'.
Free fall motion
When an object falls freely under the influence of gravity, it experiences constant acceleration. The acceleration due to gravity is denoted by 'g' and its value is approximately 9.8 m/s^2 on Earth. In this case, we are given that 'g' is equal to 10 m/s^2.
Using kinematic equations
We can use the kinematic equations of motion to solve this problem. One of the important equations for free fall motion is:
s = ut + (1/2)gt^2
Where,
s = distance traveled
u = initial velocity (which is 0 as the stone starts from rest)
t = time taken
g = acceleration due to gravity
In the last second of motion, the time taken is 1 second. So we can rewrite the equation as:
s = (1/2)g + (1/2)g
Calculating the distance
Given that the stone travels a distance of 9h/25 in the last second, we can substitute this value in the equation:
9h/25 = (1/2)(10) + (1/2)(10)
9h/25 = 10
Solving for h
To solve for 'h', we can multiply both sides of the equation by 25:
9h = 250
Now, dividing both sides by 9:
h = 250/9
h = 27.78 m
Answer
The value of 'h' is approximately 27.78 meters. However, none of the given options match this value. Therefore, there may be an error in the options provided.
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Community Answer
A stone falls freely from rest from a height h and it travels a distan...
Step 1: Equations of motion for Last second
Let the total time of fall is 't' s, in the last second (tth second) displacement is 9h/25 Initial speed u=0 ; Acceleration a = g
Using expression for displacement in nth second (Taking downward positive)
Step 2: Equations of motion for whole motion
(Taking downward Positive)
Step 3: Equation solving
From equation (1) and (2)
From equation (2)
Hence the value of h is 125 m.
Using expression for displacement in nth second (Taking downward positive)
Step 2: Equations of motion for whole motion
(Taking downward Positive)
Step 3: Equation solving
From equation (1) and (2)
From equation (2)
Hence the value of h is 125 m.
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A stone falls freely from rest from a height h and it travels a distance of 9h/25in the last second. The value of h is:(Take g = 10 m/s2):a)145 mb)100 mc)125 md)200 msCorrect answer is option 'C'. Can you explain this answer?
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