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

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In summary, the conversation discusses a method of determining the exact height of a cliff by throwing an object off and timing its fall, followed by using math to calculate the height. The asker is specifically looking for a detailed explanation of the math involved, as they are not a math expert. Trigonometry is mentioned as a potential method for calculating the height, and the use of GPS is suggested as an easier alternative.
  • #1
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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  • #2
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.
 
  • #3
Make sure if you use mark's equation that the rock is either dropped or thrown straight ahead.
 
  • #4
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.
 
  • #5
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.
 

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

How do you find the initial velocity of the object?

The initial velocity can be found by measuring the horizontal distance the object travels, the height of the object, and the time it takes for the object to reach the ground. Using the equation v = d/t, where v is the initial velocity, d is the horizontal distance, and t is the time, you can calculate the initial velocity of the object.

What is the equation for calculating the height of the object?

The equation for calculating the height of the object is h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the object to reach the ground. This equation assumes that the initial velocity of the object is 0.

Can the calculation be affected by air resistance?

Yes, air resistance can affect the calculation of the height of the object. Air resistance can slow down the object and cause it to take longer to reach the ground, which would result in a higher calculated height. However, this effect is usually negligible for objects thrown at low velocities.

Do you need to know the mass of the object for this calculation?

No, the mass of the object is not needed for this calculation. The height of the object only depends on the initial velocity, acceleration due to gravity, and time it takes for the object to reach the ground.

Can this method be used for any object?

Yes, this method can be used for any object as long as it is thrown at a consistent initial velocity and the height of the object and the time it takes to reach the ground can be accurately measured.

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