Will three objects land at the same time when dropped from the same height?

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

Posted on

The time t an object takes to fall from a height h depends on h, not on its mass. The formula to determine that time is as follows:

`t=sqrt((2h)/g)`

where g is the acceleration due to gravity and it's a constant equal to 9.8 `m/s^2 ` or 32.17`ft/s^2 ` .

Thus if three objects with different masses are dropped from the same height, they will all land at the same time.

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atsuzuki | (Level 1) Adjunct Educator

Posted on

The answer to this question is: It depends on the context and on the setting for the experiment, that is in what conditions and what type of objects are used. If the experiment is set in vacuum or (nearly vacuum), then no matter the form, composition, size, mass of the three objects, they all will land at the same time as long as they are dropped simultaneously.

However, if the experiment is done in our atmosphere, then the form, and the size of the object will play a key role in the time of landing, because then the force of friction exerted by air on the object may be very great (like on an open sheet of paper) as compared to the force of friction exerted on the same sheet of paper, but now all crushed to form a ball like object. It is not difficult to see that these two objects with (same mass but) distinct forms will have different times of landing. So the conditions of the experiment is crucial to say what happens.

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chrisyhsun | Student, College Freshman | (Level 1) Salutatorian

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This depends on the nature of the three objects and the context under which you are examining the objects. As other answers have stated, if you look at the three objects in an ideal setting and ignore resistance, they will all land at the same time, as shown through the calculations. However, if you are looking at this from a practical standpoint, the three objects may or may not land all at the same time. If they are the exact same objects or if the only difference among the three is in the mass, the objects will still land all at the same time because they are assumed to have the same surface area and therefore experience the same amount of air resistance. However, say you are looking from a practical standpoint (experimental) and three pieces of paper – two of which are flat and one of which is crushed into a ball. Even though the masses of the three objects are the same, because the two flat sheets have greater surface area, they will experience more air resistance and thus land after the crumpled paper.

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ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

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Yes, the three objects (despite their varying masses) will all land at the same time. 

One kinematics equation to look at is:

`x - x_0 = v_0t + 1/2at^2`

By manipulating the equation, you can set the equation to t (time). Initial velocity (v0) can be ruled out along with initial distance (x0).

`t = sqrt ((2x)/a)`

As you can see, mass is not a factor/variable in determining time when it comes to gravity.

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nav1996 | Student | (Level 1) Honors

Posted on

Ignoring the effects of air resistance, the amount of time it takes for an object to hit the ground is only proportional to its height, not the mass.

One of the basic equations that describes motion is as follows:

d = (vi)t + (1/2)(a)(t^2)

d = distance traveled
vi = initial velocity
a = acceleration
t = time

In the case described in your problem, the objects are simply being dropped meaning that they have an initial velocity (vi) of 0. This leaves us with:

d = (1/2)(a)(t^2)

Solving for t, we get:

sqrt(2d/a) = t

With this, we can see that the distance and acceleration are the only things that determine the amount of time it takes for objects to fall. The acceleration in this case of "free fall" is equal 9.8 m/s^2 for all objects on earth and as described in the problem, all objects fall from the same height, making the value of t equal in all three instances. 

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eli468 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Yes, the objects will all land at the same time.

The reasoning for this is because free-falling objects only have gravity working on them. They do not have any air resistance fighting against them. If something weighs more than another item dropped, it would have to have a large amount of air resistance to land at a separate time. A great description to make more sense of why this happens is this:

"The acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. Thus, the greater force on more massive objects is offset by the inverse influence of greater mass. Subsequently, all objects free fall at the same rate of acceleration, regardless of their mass."

Sources:
atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

Yes they will, it is the law of gravity but because of the air resistance on earth it is not really "true" but on the moon it would be the exact same rate

tyler-k's profile pic

tyler-k | Student, Grade 12 | (Level 1) Salutatorian

Posted on

In the case that there is not a significant amount of air resistance, any three objects will land at the same time if dropped at the same time. The website below has a really interesting (and funny) explanation of how and why this happens.

Sources:

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