Water is filled in a uniform container of area of cross section `A`. A hole of cross section area a `( lt lt A)` is made in the container at a height of `20 m` above the base. Water streams out and hits a small block on surface at some distance from container. Block is moved on surface in such a way that stream always hits the block. The initial velocity of the block (in `m//s`) is (Given `(a)/(A)=(1)/(20)`). (Take `g=10ms^(-2)`)

Explanation

Velocity of efflux `v=sqrt(2gy)`
Range `x=sqrt(2gy)xxsqrt((2h)/(g))`
The velocity of the block must be `((dx)/(dy))`
`:. V_(b)=(dx)/(dt)=sqrt((2h)/(g))xxsqrt(2g)xx(1)/(2sqrt(y))(dy)/(dt)`
`V_(b)=(sqrt(h))/(sqrt(y)).(dy)/(dt)`….(`i`)
Using equation of continuity
`(Ady)/(dt)=asqrt(2gy)`......(`ii`)
equation (`i`) and (`ii`)
`V_(b)=sqrt((h)/(y))xx(a)/(A)sqrt(2gy)`
`V_(b)=sqrt(2gh)xx(a)/(A)=20xx(1)/(20)=1ms^(-1)`.