Calculating Free Fall Time Using "g" Only

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Homework Help Overview

The discussion revolves around calculating the time it takes for a free-falling object to reach the ground from an unknown height, using only the acceleration due to gravity (g) and without introducing additional constants. The original poster expresses difficulty in formulating an equation that meets these criteria.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations of motion, including displacement and velocity, and question how to relate these to the unknown height and time of fall. There is a focus on Newton's second law and the implications of mass in free fall. Some participants suggest using the relationship between the time of fall and the time taken for sound to travel back after the object hits the ground.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have offered equations and hints, while others are questioning the assumptions and constraints of the problem. There is recognition of the complexity of the problem, and some participants express uncertainty about the correct interpretation of the variables involved.

Contextual Notes

Participants note that the problem is part of a computed homework system that restricts the introduction of new variables not mentioned in the original problem statement. There is also mention of the requirement to calculate the height of the cliff, which adds to the complexity of the discussion.

Ahmedstein
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Ok guys, I really need your help on this one. A free faling object from an unknown height. How can I get an equation to calculate the time that takes that object to reach the ground with only using "g" (free fall acceleration) and no other constant.

Pleease, if you love The Beatles, you'd help me. I tried everything and couldn't do it.
 
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Ahmedstein said:
Ok guys, I really need your help on this one. A free faling object from an unknown height. How can I get an equation to calculate the time that takes that object to reach the ground with only using "g" (free fall acceleration) and no other constant.

Pleease, if you love The Beatles, you'd help me. I tried everything and couldn't do it.

...not just anybody? :biggrin:

Well, write down the equation of displacement and the equation of velocity of the object. Use a condition in every equation, and you can retrieve the time. (Hint 1: what is the velocity when it hits the ground? ; Hint 2: what is the displacement at the same time? )
 
Set up Newton's 2.law with "m" signifying the (unknown) mass.
See what you can do with that m!
 
@radou:The displacement when it hits the ground is the height from which the object was dropped, which I cannot use. and the velocity at that point is soo unknown.

@arildno: Mass does not matter in free fall

So the conclusion is: initial velocity is ZERO, accerleration is (-g) and t=?? .. maan, that's the most difficult problem, I've ever dealt with
 
Set up Newton's 2.law! In symbols please!
 
arildno said:
Set up Newton's 2.law! In symbols please!

F=m a :confused:
 
arildno said:
Set up Newton's 2.law with "m" signifying the (unknown) mass.
See what you can do with that m!

dude, I'm not supposed to add new variables that are not mentioned in the problem.
 
Ahmedstein said:
F=m a :confused:
Quite so!
And, what is F in this case?
 
Ahmedstein said:
dude, I'm not supposed to add new variables that are not mentioned in the problem.
It doesn't say that explicitly, does it?
 
  • #10
arildno said:
Quite so!
And, what is F in this case?

the force of gravity?! :cry:
 
  • #11
Which in symbols can be written as??
 
  • #12
arildno said:
It doesn't say that explicitly, does it?

actually, it does. It is a computed homework system and if I use variables that are not in the problem it says "the answer doesn't not depend on that variable"

for example I tried that:
h is height or displacement
h= -0.5gt(squared)
t= square root of (2h/g)

I know it's a square root of a negative number, but I couldn't think of anything else. and it said "the correct answer doesn't depend on h" ... actually I am supposed to calculate the height. I just didn't tell you the whole problem.
 
  • #13
Ok, here it is. An object was dropped from the top of a cliff and the dropper heard the sound after (t) time. ok, and it's given in the question that speed of light is V, and free fall accerelation is a, and I should find the height of the cliff, so I figured out that I should use h= V * t, but I should subtract the time that took the object to reach the ground from the given (t), as the given t should equal (time that takes the object to hit the ground + time that takes sound to reach the top of the buiding to be heard) am I right?
 
  • #14
Ahmedstein said:
Ok, here it is. An object was dropped from the top of a cliff and the dropper heard the sound after (t) time. ok, and it's given in the question that speed of light is V, and free fall accerelation is a, and I should find the height of the cliff, so I figured out that I should use h= V * t, but I should subtract the time that took the object to reach the ground from the given (t), as the given t should equal (time that takes the object to hit the ground + time that takes sound to reach the top of the buiding to be heard) am I right?

Yes, sounds right.
 
  • #15
so it is h= v (t- ?) :(
 
  • #16
Ahmedstein said:
so it is h= v (t- ?) :(

Let's slow down. The equation for the y-displacement (which is the only direction of displacement, btw) is y(t) = y0 - 1/2*g*t^2, where y0 is the height of the cliff, you may call it h, if you want, doesn't really matter. So, you know the time, let's call it t1. So, we can write y(t1) = y0 - 1/2*g*t1^2. Now, what does y(t1) equal?
 
  • #17
shouldn't it be y(t) = V0 - 0.5 g t^2 , where V0 is the initial velocity, which in this case is equal to zero
 
  • #18
:rolleyes: :frown: :cry:
 
  • #19
Ahmedstein said:
shouldn't it be y(t) = V0 - 0.5 g t^2 , where V0 is the initial velocity, which in this case is equal to zero

In general, y(t) = y0 + v0*t -1/2*g*t^2. So, yes, the initial velocity v0 equals zero, and you're left with y(t) = y0 - 1/2*g*t^2.
 
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  • #20
aaaahhhhhhh
 
  • #21
Does anyone have anything to say?
 
  • #22
Ahmedstein said:
Does anyone have anything to say?

Everything is said. :smile: As stated, y0 - 1/2*g*t^2 = 0, where y0 is your height, and t is the time you calculated.
 
  • #23
but dude, h is required in the problem, if I use this the answer is going to be:

h = V (t - square root of 2h/g)

that doesn't make any sense
 
  • #24
Ahmedstein said:
but dude, h is required in the problem, if I use this the answer is going to be:

h = V (t - square root of 2h/g)

that doesn't make any sense

What doesn't make any sense? h - 1/2*g*t^2 = 0 implies h = 1/2*g*t^2, and you know the time t, so just calculate h!
 
  • #25
Ahmedstein said:
Ok, here it is. An object was dropped from the top of a cliff and the dropper heard the sound after (t) time. ok, and it's given in the question that speed of light is V, and free fall accerelation is a, and I should find the height of the cliff, so I figured out that I should use h= V * t, but I should subtract the time that took the object to reach the ground from the given (t), as the given t should equal (time that takes the object to hit the ground + time that takes sound to reach the top of the buiding to be heard) am I right?

please read it again and tell me what that (t) represents

the (t) in the equation (h = 0.5 g t^2) is the objects time

it's not the same as the (t) in the problem
 
  • #26
You're right, I was a bit sloppy, I'm sorry. :smile: OK, let's start again. The first equation is h - 1/2*g*t1^2 = 0, where t1 is the time it took for the object to reach the ground. Now, you know that h = V*(t' - t1), where t' = (t) (the time until you heard the sound). So, you get the equation V*(t' - t1) = 1/2*g*t1^2, from which you can calculate t1.
 
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  • #27
I think this problem is a bit advanced.Anyway, Thanks for the help everyone. You guys are great.
 

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