How does halving the time affect the distance traveled by a falling object?

In summary: The answer is "moving half the distance in half the time would be right for uniform velocity", which is what the original problem stated.
  • #1
M. M. Fahad Joy
25
2

Homework Statement



If a falling object overcome 72 metres in 6 second, how much distance it overcame in first 3 second.

Homework Equations


s = ut+(at^2)/2

The Attempt at a Solution


Here,
s = 72 m
u = 0
t = 6s
a = ?
We know,
s = ut+(at^2)/2
Or, 72 = 0*6 + (a*6^2)/2
Or, 72 = 36a/2
Or, 72 = 18a
Or, a = 4 m/s

In the second part,
u = 0
t = 3s
a = 4 m/s^2
s = ?
Again,
s = ut+(at^2)/2
= 0*t + (4*3^2)/2
= (4*9)/2
= 36/2
= 18 m (ans.)
 
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  • #2
M M FAHAD JOY said:

Homework Statement



If a falling object overcome 72 metres in 6 second, how much distance it overcame in first 3 second.

Homework Equations


s = ut+(at^2)/2

The Attempt at a Solution


Here,
s = 72 m
u = 0
t = 6s
a = ?
We know,
s = ut+(at^2)/2
Or, 72 = 0*6 + (a*6^2)/2
Or, 72 = 36a/2
Or, 72 = 18a
Or, a = 4 m/s

In the second part,
u = 0
t = 3s
a = 4 m/s^2
s = ?
Again,
s = ut+(at^2)/2
= 0*t + (4*3^2)/2
= (4*9)/2
= 36/2
= 18 m (ans.)
You have apparently assumed the falling object is on another planet or somewhere in space above the Earth's surface where the acceleration of gravity is not the same as it is at Earth's surface. Since a object would fall more than 72m in 6s near Earth's surface, your assumption seems reasonable, and you have correctly worked out the result based on that assumption. But are your sure that was what was intended in the original question?
 
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  • #3
tnich said:
You have apparently assumed the falling object is on another planet or somewhere in space above the Earth's surface where the acceleration of gravity is not the same as it is at Earth's surface. Since a object would fall more than 72m in 6s near Earth's surface, your assumption seems reasonable, and you have correctly worked out the result based on that assumption. But are your sure that was what was intended in the original question?
It's from my school exam question.
It's about falling object on Earth. But the gravity of Earth is 9.8 as I know.
We know that the gravity doesn't depend on mass. But for the friction of air reduces the acceleration of gravity. So it a problem me seeing the first law of falling bodies.
 
  • #4
M M FAHAD JOY said:
It's from my school exam question.
It's about falling object on Earth. But the gravity of Earth is 9.8 as I know.
We know that the gravity doesn't depend on mass. But for the friction of air reduces the acceleration of gravity. So it a problem me seeing the first law of falling bodies.
The force that air resistance applies to a falling body (called drag) depends on the speed of the falling body. So you could not solve the problem by assuming drag is constant. You might look at the original problem statement and if there is anything you missed.
 
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  • #5
tnich said:
The force that air resistance applies to a falling body (called drag) depends on the speed of the falling body. So you could not solve the problem by assuming drag is constant. You might look at the original problem statement and if there is anything you missed.
I have checked it again. It is ok.
 
  • #6
M M FAHAD JOY said:
I have checked it again. It is ok.
In the problem statement you have written "overcome [a distance]". That is not a common expression. I assume that is your translation of the original problem. What do you think it means?
 
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  • #7
tnich said:
In the problem statement you have written "overcome [a distance]". That is not a common expression. I assume that is your translation of the original problem. What do you think it means?
I am not so well in English. I have translated it from my own language. That's the problem.
 
  • #8
M M FAHAD JOY said:
I am not so well in English. I have translated it from my own language. That's the problem.
Do you think the object could have started out going upward, reached a maximum height and then fallen?
 
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  • #9
tnich said:
Do you think the object could have started out going upward, reached a maximum height and then fallen?
I didn't mean to criticize your English. I meant to ask if "overcome 72 m" could mean something different than "fall 72m".
 
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  • #10
tnich said:
I didn't mean to criticize your English. I meant to ask if "overcome 72 m" could mean something different than "fall 72m".
Yes, the translation will be fall 72 metres.
By the way, it was an MCQ.
a) 36m b) 24m c) 18m d) 8m

Most of my friends answered 36 metres. But I have answered 18 metres. That's my confusion.
 
  • #11
M M FAHAD JOY said:
Most of my friends answered 36 metres.
Then they fell into the trap.
Moving half the distance in half the time would be right for uniform velocity, but for uniform acceleration from rest it is a quadratic, so a quarter of the distance in half the time.
 
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  • #12
haruspex said:
Then they fell into the trap.
Moving half the distance in half the time would be right for uniform velocity, but for uniform acceleration from rest it is a quadratic, so a quarter of the distance in half the time.
Are you sure, quarter of the distance in half time?
 
  • #13
M M FAHAD JOY said:
Are you sure, quarter of the distance in half time?
½at2. What happens to that if you halve t? Note, this is only for falling from rest.
 
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  • #14
haruspex said:
½at2. What happens to that if you halve t? Note, this is only for falling from rest.
Ok, Thanks.
 

Related to How does halving the time affect the distance traveled by a falling object?

What are the "Laws of Falling Bodies"?

The "Laws of Falling Bodies" are a set of principles that describe the motion of objects as they fall towards the Earth's surface. These laws were first proposed by Sir Isaac Newton in the 17th century and are still used today to understand and predict the behavior of falling objects.

What is the first law of falling bodies?

The first law of falling bodies, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force. This means that a falling object will continue to fall at a constant speed unless something, like air resistance or another force, slows it down.

What is the second law of falling bodies?

The second law of falling bodies states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the more force that is applied to an object, the greater its acceleration, and the more massive an object is, the less it will accelerate.

What is the third law of falling bodies?

The third law of falling bodies, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when an object falls towards the Earth due to the force of gravity, the Earth also exerts an equal and opposite force on the object, causing it to accelerate towards the Earth's surface.

How do these laws apply to real-life scenarios?

The laws of falling bodies are used in many real-life scenarios, such as predicting the trajectory of a thrown ball, understanding the motion of a roller coaster, and calculating the speed and impact of a falling object. These laws also play a crucial role in the study of gravity and planetary motion in the field of astronomy.

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