How to calculate the height of something by throwing an object off it?

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Discussion Overview

The discussion revolves around methods to calculate the height of a cliff by throwing an object off it and timing its fall. Participants explore various mathematical approaches and practical considerations related to this problem, including the use of equations and trigonometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using the equation h = 16t² to calculate height, where t is the time in seconds and h is the height in feet.
  • Another participant emphasizes that the object should be either dropped or thrown straight ahead for the equation to be applicable.
  • Some participants propose alternative methods, such as measuring the distance from the base of the cliff and applying trigonometry to determine the height.
  • There is mention of using GPS technology as a modern tool to assist in measuring distances more accurately.

Areas of Agreement / Disagreement

Participants present multiple methods for calculating height, including the use of the time of fall and trigonometry. There is no consensus on a single best approach, as various techniques are discussed.

Contextual Notes

The discussion does not resolve the accuracy or reliability of the different methods proposed, nor does it address potential errors in timing or measurement.

Bellabob
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I go rock climbing a lot with my BSA troop, and my friends and I can only estimate the height. I want to know the exact height. Considering I do not have a ruler long enough to measure the height of the cliff, I know there is a way to throw an object off the cliff (say, a rock), time how long it takes to hit the ground, and then do some math and then you have the height.

I want to know how to do the math. Please be detailed with your answer, because I'm 15 and not really a math genius (I'm good, but not THAT good).

Thanks.
 
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Bellabob said:
I go rock climbing a lot with my BSA troop, and my friends and I can only estimate the height. I want to know the exact height. Considering I do not have a ruler long enough to measure the height of the cliff, I know there is a way to throw an object off the cliff (say, a rock), time how long it takes to hit the ground, and then do some math and then you have the height.

I want to know how to do the math. Please be detailed with your answer, because I'm 15 and not really a math genius (I'm good, but not THAT good).

Thanks.

h = 16t2
t is in seconds and h is in feet.
 
Make sure if you use mark's equation that the rock is either dropped or thrown straight ahead.
 
BTW, there are other ways that might have less error than estimating a time of a second or two.

You can figure out how far you are from the base of the cliff and use trig to calculate its height.
 
DaveC426913 said:
You can figure out how far you are from the base of the cliff and use trig to calculate its height.

Damn you beat me. :frown:
But yes, trig is how it has always been down in the past. And we have GPS now, so it's easier too.
 

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