EPTTo determine the height of a building a stone is dropped from the top of the building and into a lake. It takes 6.8 seconds for the stone to hit the water. What is the height of the building?
[H]Calculus
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dancefayedance!~
396 Posts
To determine the height of a building a stone is dropped from the top of the building and into a lake. It takes 6.8 seconds for the stone to hit the water. What is the height of the building? | ||
Xeofreestyler
Belgium6774 Posts
Seeing how a = 9,81 m/s² which is the acceleration of the object You only have to put it in your formula and voila | ||
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dancefayedance!~
396 Posts
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ToT)SiLeNcE(
Germany590 Posts
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HonkHonkBeep
China353 Posts
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dancefayedance!~
396 Posts
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ilovejonn
Canada2548 Posts
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Eti307
Canada3442 Posts
On October 18 2007 04:52 dancefayedance!~ wrote: it's in a calculus book :/ It's still not calculus, this is basic physics | ||
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dancefayedance!~
396 Posts
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IntoTheWow
is awesome32277 Posts
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randombum
United States2378 Posts
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IntoTheWow
is awesome32277 Posts
![[image loading]](http://img138.imageshack.us/img138/390/asdsddq5.gif) | ||
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IntoTheWow
is awesome32277 Posts
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azndsh
United States4447 Posts
v(t) = g*t, where g = 9.8 m/s^2 solve for h, such that integral from 0 to t_h of {v(t) dt} = h, where t_h is the time it takes to hit the water: 6.5s of course, the left side, you get integral from 0 to t_h of {g*t dt} = 1/2 g*t^2 evaluated from 0 to t_h = 1/2 g * (t_h)^2 So h = 1/2 * (9.8 m/s^2) *(6.5s)^2 | ||
Insane
United States4991 Posts
<hr> If you want to solve it in a calculus way consider it as a series of initial value integrations: Let p(t) be position, v(t) be velocity, and a(t) be acceleration We know: p(6.8) = 0 v(0) = 0 a = -9.8 v = (int)a dt = -9.8t + C Plug in v(0) = 0 0 = -9.8(0) + C therefore C = 0 p = (int)v dt = .5 * -9.8t² + C' (C' to indicate that it's different from the C above) = -4.9t² + C' Plug in p(6.8) = 0 0 = -4.9(6.8²) + C' C' = 226.576 Now check out p(0) for the initial height. p(0) = -4.9(0²) + 226.576 Therefore p(0) = 226.576 (Note the use of negatives throughout problem. Otherwise you will end up with your height as negative  . The important thing is it to be consistent with the negatives, and I view up as positive and down as negative)Also my answer is slightly different from theirs since I used 9.8 instead of 9.81 (which admittedly is slightly less accurate, but 9.8 / 2 is nicer than 9.81 / 2  )Edit: Obviously this is a simple physics problem btw, and no I would not solve it this way if I actually wanted to get the answer. However, I assumed he wasn't supposed to just plug it into one of the physics equations. Sidenote: speaking of physics, C is initial velocity and C' is initial position. | ||
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ilovejonn
Canada2548 Posts
>____> | ||
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Meta
United States6225 Posts
On October 18 2007 09:33 ilovejonn wrote: Shitt...so many smart guys on TL.net, next time I gotta bring up some homework questions too.... >____> haha, last year we had a crusade against homework threads, although now that there's a blog feature i don't think that would be much of a big deal anymore  | ||
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dancefayedance!~
396 Posts
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Chill
Calgary25989 Posts
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fight_or_flight
United States3988 Posts
On October 18 2007 10:28 Chill wrote: wtf where did hotbid even post in this blog? Ha, I was just about to ask....was typing... edit: isn't hotbid a law major? does he know calculus too?? | ||
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