Answer
The lake has a depth of $~~38.1~m$
Work Step by Step
We can find the velocity after the ball drops $5.20~m$:
$v^2 = v_0^2+2ay$
$v^2 = 0+2ay$
$v = \sqrt{2ay}$
$v = \sqrt{(2)(9.80~m/s^2)(5.20~m)}$
$v = 10.1~m/s$
We can find the time it takes the ball to fall $5.20~m$:
$y = \frac{1}{2}at^2$
$t = \sqrt{\frac{2y}{a}}$
$t = \sqrt{\frac{(2)(5.20~m)}{9.80~m/s^2}}$
$t = 1.03~s$
We can find the time it takes the ball to fall after it reaches the top surface of the water:
$t = 4.80~s-1.03~s = 3.77~s$
We can find the depth of the lake:
$d = (10.1~m/s)(3.77~s) = 38.1~m$
The lake has a depth of $~~38.1~m$.
