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

Answer

B

Explanation

`R=vt`
`R=sqrt(2gd)sqrt((2h)/(g))`
`d=(R^(2))/(4h)`
Applying Bernoulli theorem
`(P+(mg)/(A))+(1)/(2)rho(0)^(2)+rhogh=P+(1)/(2)rhov^(2)+0`
`(mg)/(A)+rhogh=(1)/(2)rhov^(2)`
`(10xx10)/(0.1)+1000xx10xx0.5=(1)/(2)xx1000xxv^(2)`
`1000+5000=500v^(2)`
`v=2sqrt(3)m//simpliesv=3.4m//s`