A water barrel stands on a table of height `h`. If a small holes 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 Torricelle.s theorem, `v= sqrt((2gd))`
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)) = 2 sqrtdh or d = (R^(2))/(4h)`