Calculating Free Fall Time Using "g" Only

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SUMMARY

The discussion revolves around calculating the time it takes for a free-falling object to reach the ground using only gravitational acceleration "g" and without additional constants. Participants emphasize the importance of Newton's second law, where the force of gravity is represented as F = m * a, and clarify that mass does not affect free fall. The key equation derived is h = 1/2 * g * t^2, which allows for the calculation of height based on time of fall, with the final conclusion that the height can be expressed as h = V * (t' - t1), where t' is the total time until the sound is heard and t1 is the time taken for the object to hit the ground.

PREREQUISITES
  • Understanding of Newton's second law (F = m * a)
  • Knowledge of free fall acceleration (g)
  • Familiarity with kinematic equations for motion
  • Basic grasp of sound travel time and its relation to height
NEXT STEPS
  • Study kinematic equations in detail, particularly h = 1/2 * g * t^2
  • Explore the relationship between sound speed and time delay in free fall problems
  • Learn about the derivation of equations of motion under constant acceleration
  • Investigate advanced physics problems involving free fall and sound propagation
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Students in physics, educators teaching mechanics, and anyone interested in solving problems related to free fall and gravitational acceleration.

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.
 
Last edited:
  • #27
I think this problem is a bit advanced.Anyway, Thanks for the help everyone. You guys are great.
 

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