What is the relationship between time and height in object free fall?

In summary, When an object falls freely, the time it takes to reach a certain height is not directly proportional to the height itself. In summary, the conversation is about someone who is trying to teach themselves physics in preparation for taking college classes. They have a specific problem they are having trouble with and are seeking help. The problem involves an object falling from a certain height and the time it takes to reach different points. The solution uses the formula h=1/2gt^2 and explains how certain numbers, such as 0.707, become familiar in physics. The summary also mentions that the time it takes for an object to fall from a certain height is not directly proportional to the height itself.
  • #1
BrendanB
1
0
Hello,
I am new to this site. I am currently active duty military (navy) and I am trying to teach myself physics because when I get the time, I would like to take some college physics classes. I downloaded a few physics books online and I am trying to page through them. I am having some trouble figuring out this problem. I feel like a complete idiot because I have the correct answer right in front (teacher solution manual downloaded too) of me and still can't figure it out! Anyways, here is the problem and the correct answer (below). Any help you can offer would be appreciated.

Homework Statement



An object falls freely from height h. It is released at time
zero and strikes the ground at time t. (a) When the object
is at height 0.5h, is the time earlier than 0.5t, equal to 0.5t,
or later than 0.5t? (b) When the time is 0.5t, is the height
of the object greater than 0.5h, equal to 0.5h, or less than
0.5h? Give reasons for your answers.

Homework Equations


The Attempt at a Solution


I understand the formula h=1/2gt^2, but what I don't understand is where they are getting the "0.707t" when they plug in 0.5h.
I also don't understand the second equation where they are getting 0.25h4. Answer
With h=1/2gt^2
(a)0.5h=1/2g(0.707t)^2
(b)The distance fallen is 0.25h=1/2g(0.5t)^2. The elevation is 0.75h, greater than 0.5h.
 
Last edited:
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  • #2
As you do more physics, certain numbers will become familiar. 0.707= 1 over the square root of two. In other words, due to the "t squared" in the formula you mentioned, the height from which an object is released, and the time it takes for the object to hit the ground are not "directly proportional." That is, compared to the first initial test (drop from height H, and record time, t), if you cut the height in half (H/2), the time will not be t/2, but t/√2. If you cut the height to a third (H/3), the time will not be t/3, but t/√3, etc. And if you triple the height (3H), the time will be t*√3.
 

1. What is object free fall physics?

Object free fall physics is the study of the motion of objects that are falling under the influence of gravity without any external forces acting on them. It involves understanding the forces, velocities, and accelerations involved in an object's free fall.

2. What is the acceleration due to gravity?

The acceleration due to gravity is a constant value of 9.8 m/s² (meters per second squared) on Earth. This means that every second, an object in free fall will increase its velocity by 9.8 m/s.

3. How does air resistance affect object free fall?

Air resistance, also known as drag, will slow down the acceleration of an object in free fall due to the opposing force it creates. This means that an object's acceleration will decrease as it falls, and eventually reach a constant velocity known as the terminal velocity.

4. What is the difference between mass and weight in object free fall?

Mass is a measure of the amount of matter in an object, while weight is the force of gravity acting on an object's mass. In object free fall, mass remains constant, but weight will change as the object moves closer to or further away from the Earth's center of gravity.

5. How does the height of an object affect its free fall?

The height of an object will affect its free fall in terms of the time it takes to reach the ground. The higher the initial height, the longer it will take for the object to fall. However, the acceleration due to gravity and the object's final velocity will remain constant regardless of the initial height.

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