A tank is filled with water upto a height H. A hole is punched in one of the walls at a depth `h_1` below the water surface. (a) Find the distance from the foot of the wall at which the stream strikes the floor. (6) Is it possible to make second hole at another depth so that this second stream also has the same range? If so find its depth ?

Explanation

Using Torricelli.s theorem the velocity of efflux ` v= sqrt( 2gh ) `
Let R be the horizontal distance covered in a time inerval t.
` " " R= vt = sqrt( 2gh_1)` t
The vertical height covered in the time t is `H - h_1`
` " " s = ut +(1)/(2) at ^(2) = 0 xx t +(1)/(2) gt^(2)`
` " " t= sqrt((2s)/(g))= sqrt( (2(H-h_1))/( g))`
` R = sqrt( 2gh_1) xx sqrt((2(H-h_1))/( g)) =2 sqrt(h_1(H-h_1))`
Let the second hole be directed at a depth h, below the free surface of water. Then the new range is ` 2sqrt(h_2( H-h_2)).` by the above procedure.
` " "R = 2 sqrt( h_1( H-h_1)) = 2 sqrt( h_2(H-h_2))`
` " " h_1H= h_1^(2) =h_2 H- h_2^(2)`
`( h_2-h_1) (H-h_2-h_1) = 0 `
` " " h_2= h_1 or h_2= H-h_1`
The second hole is at a depth `H- h_1` from the free surface of water so that its also gives the same range.