Answer
The lake is 29.7 meters deep.
Work Step by Step
We can find the speed when the ball hits the water;
$v^2 = v_0^2+2ay = 0+2ay$
$v = \sqrt{2ay} = \sqrt{(2)(9.80~m/s^2)(5.0~m)}$
$v = 9.9~m/s$
We use this speed to find the depth $d$ of the lake:
$d = v~t = (9.9~m)(3.0~s)$
$d = 29.7~m$
The lake is 29.7 meters deep.
