AAMC 5 Q45

[labqi]

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Hey guys
I had a quick question regarding question 43 in aamc 5.
http://mysowar.files.wordpress.com/2011/05/43.jpg
That was from a previous post on the website.

My question is: why can't i figure the question out as follows:
v = sqrt(2gh)

vMiddle = sqrt (2g10) = sqrt (200)
vTop = sqrt(2g20) = sqrt (400)

thus 10sqrt2 / 20 = sqrt2/2

I don't know what I am missing
I get different answers when i use a different approach: sqrt (2-10-10 / 2-10-20) = sqrt 1/2

why am i getting different answers?

 

[Chrisz]

Bro vmiddle/vtop= 1/sqr(2), which means vmiddle is smaller by sqr(2), so answer D. sq(200)=10sq(2) sq(400)=10sq(4)
Actually Sq(200)/sq(400)=sq(200/400)=sq(1/2)=1/sq(2)