A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R from the table. What is the depth of water in the barrel?
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a
R2h
b
R22h
c
R24h
d
4R2h
answer is C.
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Detailed Solution
From Torricelli's theoremv = 2gd ------(i)where y is horizontal velocity and d is the depth of water in barrel.Time t to hit the ground is given byh = 12gt2 or t = 2hg∴ R = vt = (2gd)2hg = 2dh (Using (i))∴ R2 = 4dh or d = R24h