Calculating Distance From a Falling Stone

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SUMMARY

The discussion focuses on calculating the distance a stone falls in a cavern using the formula s = (1/2)(-gt^2), where g represents the acceleration due to gravity. The participants agree that if two objects accelerate at the same rate, knowing the time it takes for the stone to hit the bottom allows for an estimation of the distance fallen. The conversation highlights the importance of considering initial velocity and the impact of height on the results, emphasizing that while the calculation provides an estimate, it does not need to be exact.

PREREQUISITES
  • Understanding of basic physics concepts, specifically gravitational acceleration.
  • Familiarity with the kinematic equation for uniformly accelerated motion.
  • Knowledge of the concept of initial velocity in free fall scenarios.
  • Basic mathematical skills for manipulating algebraic equations.
NEXT STEPS
  • Research the effects of air resistance on falling objects.
  • Explore advanced kinematic equations for varying initial velocities.
  • Learn about the acceleration due to gravity variations at different altitudes.
  • Investigate practical applications of free fall calculations in physics experiments.
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Students studying physics, educators teaching kinematics, and anyone interested in practical applications of gravitational motion calculations.

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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The formula is simple:
assuming zero initial velocity, the distance, s, fallen is:
s = (1/2)(-gt^2)
 

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