Chapter 6 - Dynamics I: Motion Along a Line - Exercises and Problems - Page 164: 51

Depth of the lake is $30m$

let $v$ be the velocity of ball with which it hits the water. So we have $ v^2 - u^2 =2as_1$ $u=0$ ,$s_1 = 5.0m$ and $ a= g = 9.8ms^{-2}$ thus $ v^2 - 0 = (2* 10 * 5 )m^2s^{-2} = 100m^2s^{-2}$ $v= 10ms^{-1}$ let $s_2$ be the depth of lake. therefore $s_2 = v*t$ $v= 10ms^{-1}$ and $t=3.0s$, Thus $s_2 = (10 * 3)m =30m$