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[H]Calculus

Blogs > dancefayedance!~
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1 2 Next All
dancefayedance!~
Profile Blog Joined November 2006
396 Posts
October 17 2007 19:30 GMT
#1
This question has been annoying me for about 15 minutes. I think I have an idea on how to solve it but my ADD kicks in and I lose concentration. Here is the question:
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
Profile Blog Joined June 2005
Belgium6771 Posts
October 17 2007 19:36 GMT
#2
Thats really easy
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
Graphics
dancefayedance!~
Profile Blog Joined November 2006
396 Posts
October 17 2007 19:36 GMT
#3
the problem is I don't have the formula
ToT)SiLeNcE(
Profile Blog Joined February 2003
Germany590 Posts
October 17 2007 19:38 GMT
#4
h = 1/2 * g * t^2
HonkHonkBeep
Profile Blog Joined September 2007
China353 Posts
October 17 2007 19:51 GMT
#5
This is not calculus
God is cruel; sometimes he makes us live.
dancefayedance!~
Profile Blog Joined November 2006
396 Posts
October 17 2007 19:52 GMT
#6
it's in a calculus book :/
ilovejonn
Profile Blog Joined August 2007
Canada2548 Posts
October 17 2007 19:53 GMT
#7
Physics ftw.
Snowflakes in January, Heart warm like February, I wouldn't ordinarily..
Eti307
Profile Blog Joined March 2004
Canada3442 Posts
October 17 2007 19:57 GMT
#8
On October 18 2007 04:52 dancefayedance!~ wrote:
it's in a calculus book :/


It's still not calculus, this is basic physics
dancefayedance!~
Profile Blog Joined November 2006
396 Posts
October 17 2007 19:57 GMT
#9
does the answer come out to be around 293?
IntoTheWow
Profile Blog Joined May 2004
is awesome32275 Posts
October 17 2007 20:03 GMT
#10
226.8072 m
Moderator<:3-/-<
randombum
Profile Blog Joined April 2007
United States2378 Posts
October 17 2007 20:09 GMT
#11
I think it's suppose to be calculus because of differentiation/intergral relationship of Postion-velocity-accelleration.... but thats also just physics.
IntoTheWow
Profile Blog Joined May 2004
is awesome32275 Posts
October 17 2007 20:10 GMT
#12
[image loading]
Moderator<:3-/-<
IntoTheWow
Profile Blog Joined May 2004
is awesome32275 Posts
October 17 2007 20:23 GMT
#13
Maybe you used american units?
Moderator<:3-/-<
azndsh
Profile Blog Joined August 2006
United States4447 Posts
October 17 2007 21:26 GMT
#14
well, if it's in a calculus book, i'm assuming they want a calculus solution...

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
Profile Blog Joined November 2003
United States4991 Posts
Last Edited: 2007-10-17 21:49:20
October 17 2007 21:44 GMT
#15
^^^^^^^^^^^^6.8 seconds, not 6.5

<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.
ilovejonn
Profile Blog Joined August 2007
Canada2548 Posts
October 18 2007 00:33 GMT
#16
Shitt...so many smart guys on TL.net, next time I gotta bring up some homework questions too....

>____>
Snowflakes in January, Heart warm like February, I wouldn't ordinarily..
Meta
Profile Blog Joined June 2003
United States6225 Posts
October 18 2007 01:10 GMT
#17
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
good vibes only
dancefayedance!~
Profile Blog Joined November 2006
396 Posts
October 18 2007 01:12 GMT
#18
rthank you hotbid that is exactly what i needed
Chill
Profile Blog Joined January 2005
Calgary25981 Posts
October 18 2007 01:28 GMT
#19
wtf where did hotbid even post in this blog?
Moderator
fight_or_flight
Profile Blog Joined June 2007
United States3988 Posts
Last Edited: 2007-10-18 01:31:08
October 18 2007 01:29 GMT
#20
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??
Do you really want chat rooms?
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