A cylindrical tank of height $H$ is completely filled with water. On its vertical side there are two tiny holes, one above the middle at a height h₁ and the other below the middle at a depth h₂. If the jets of water from the holes meet at the same point at the horizontal plane through the bottom of the tank then the ratio $\frac{h_1}{h_2}$ is

The horizontal range of a jet of water emerging from a hole at a height h below the surface of water is given by 

                                            $R=2\sqrt{h\left(H-h\right)}$

The upper hole is at a height $\left(\frac{H}{2}+h_1\right)$ from the bottom and the lower hole is at a height $\left(\frac{H}{2}-h_2\right)$ from the bottom. Their depths from the surface are respectively $\left(\frac{H}{2}-h_1\right) and \left(\frac{H}{2}+h_2\right)$.The horizontal ranges will be equal if

            $2\sqrt{\left(\frac{H}{2}+h_1\right)\left(\frac{H}{2}-h_1\right)}=2\sqrt{\left(\frac{H}{2}+h_2\right)\left(\frac{H}{2}-h_2\right)}$

which gives h₁ = h₂ .