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?

Options

A. `(R^2)/(h)`
B. `(R^2)/(2h)`
C. `(R^2)/(4h)`
D. `(4R^2)/(h)`

Answer

C

Explanation

From Torricelli's theorem
`v = sqrt(2 gd)` ….(i)
where `v` is horizontal velocity and `d` is the depth of water in barrel.
time `t` to hit the ground is given by
`h=1/2 gt^(2) or t=sqrt((2h)/(g))`
:. `R = vt = sqrt((2gd)) sqrt((2h)/(g) = 2sqrt(dh)` (using (i))
`:. R^(2) = 4 dh or d = (R^2)/(4h)`.