Help with math

First off, dang you, Ive got work to do today!
Assume that you 'drop' the spittle and do not add any acceleration/initial velocity. [snipped all the work I was doing, going about it all wrong.] Curses to you again.

 

Well in 8 seconds it would fall 1152 feet and I dont have the time to give you the remaining feet but it would be under 9 Seconds.

 

i just reread the question and realized you want to ignore wind, not take it into consideration.

i'll leave my real-life "with-wind" response here anyway.

32 ft/sec/sec - gravity's a value of accelleration.
when calculating air resistance, surface area is important, but you're talking about a falling liquid, which makes surface area a variable.
on top of that, you're talking about new york city, the concrete jungle.

thus, the answer is, probably never.

due to the thermals (rising warm air) and resulting turbulence, the likelyhood of spit actually hitting the ground below is nearly zero: it will get blown away and probably hit either the empire state building a couple floors down or one of the surrounding buildings.​

now, without wind:

acceleration = (final speed - initial speed)/time (a=(s2-s1)/t) and speed = distance/time (v=s/t), so
a=((s2-s1)/t)/t

flip those around and you get
s = .5 at^2
flip again for
t = root(s/(s1*t - .5 a )

numbers time!

t = root( 1250 / [ 0*t - .5 * 32 ] )
t = root( 1250 / 16 )
t = root( 78.125 )
t = 8.838 seconds

 

Ok, I think I have found it.

Use the formula:
d=v₀t + ¹/₂at²

Use quadratics to turn it around to solve for what we need giving:
t = -v₀ + sqrt(v₀ + 2ad)/a

Since our initial velocity is 0 it works out nicely tho, down to: t=sqrt(2d/a).

So
t = sqrt[2(1250)/32]
= sqrt[2500/32]
= sqrt[78.125]
t = 8.84~ seconds.

Or so my addled brain says. what do I win?

 

Cool, three answers from three people going about it three different ways. And all the answers are very similar. Gotta love that. Now, who had the most correct answer.

 

It would take 8 seconds if that is in a vacuum.

I didn't use a formula just added 32 feet every second until it got to the1250.

 

mine's less right because my empire state building is 10 feet too short.

 

Easy. v = v₀ + at

v = 0 +[32*8.84)
v = 282.88 ft/sec

And a minor nitpic. Acceleration due to gravity is actually 32ft per sec per sec. Or 32^ft/_sec^2

 

And now that weve done your summerschool homework, what do we get?

 

now add wind resistance. can anyone find the terminal velocity of (i'll estimate) 3ml of spit (assume it's water) on a standard day at msl, ignoring turbulence and updrafts?

 

about 3.5 inches per second based off a large rain drop.

http://www.shorstmeyer.com/wxfaqs/float/cdtable.html

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