Calculating Distance From a Falling Stone

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In summary, the conversation discusses the use of calculating the distance of a cavern by dropping a rock and timing its fall. The formula for calculating the distance is also mentioned, and the potential for discrepancies due to factors such as initial velocity and height at which the rock is dropped is considered. Ultimately, the conversation emphasizes the importance of using this method as an estimate rather than an exact measurement.
  • #1
Interception
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Ok, so I watched a horror movie recently and they did the whole drop a rock down a cavern and see how long it took to hit the bottom. Couldn't you find the approximate distance through this? Not just a guess like "Oh that took a little bit so it's waaaay down there".

If two objects accelerate at the same rate due to the pull of gravity, if you could calculate the speed, wouldn't it pretty much be used as an assumed constant? Then if you knew the speed, all you would have to do is divide that by the time it took to hit the bottom using Speed= Distance x Time. But then again, if you were at a higher point and dropped it, wouldn't it have more space to accerlate and throw off your results? I'm just looking for an estimate, it doesn't have to be exact.
 
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  • #2
The formula is simple:
assuming zero initial velocity, the distance, s, fallen is:
s = (1/2)(-gt^2)
 

FAQ: Calculating Distance From a Falling Stone

How do you calculate the distance from a falling stone?

The distance from a falling stone can be calculated using the formula d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time the stone has been falling.

What is the acceleration due to gravity?

The acceleration due to gravity is a constant value of 9.8 meters per second squared (m/s^2) on Earth. This means that for every second an object falls, its velocity increases by 9.8 m/s.

Does the mass of the stone affect the distance it falls?

Yes, the mass of the stone does affect the distance it falls. Heavier objects have a greater force of gravity acting on them, which causes them to accelerate faster and fall further in the same amount of time compared to lighter objects.

How can air resistance affect the calculation of distance from a falling stone?

Air resistance can affect the calculation of distance from a falling stone by slowing down the stone's acceleration and therefore reducing the distance it falls. This is because air resistance creates a force that opposes the motion of the stone, acting in the opposite direction of gravity.

Can this formula be used for objects falling in a vacuum?

Yes, this formula can be used for objects falling in a vacuum. In a vacuum, there is no air resistance, so the only force acting on the object is gravity. This means that the object will accelerate at a constant rate of 9.8 m/s^2, and the distance can be calculated using the same formula d = 1/2 * g * t^2.

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