Answer
The diameter of the water flow after the water has fallen 30 cm is $1.1~cm$
Work Step by Step
We can find the speed of the water after it falls 30 cm:
$v_2^2 = v_1^2+2ay$
$v_2 = \sqrt{v_1^2+2ay}$
$v_2 = \sqrt{(0.62~m/s)^2+(2)(9.80~m/s^2)(0.30~m)}$
$v_2 = 2.50~m/s$
We can use the continuity equation to find the radius $r_2$ of the water after it falls 30 cm:
$A_2~v_2 = A_1~v_1$
$\pi~r_2^2~v_2 = \pi~r_1^2~v_1$
$r_2^2 = \frac{r_1^2~v_1}{v_2}$
$r_2 = \sqrt{\frac{v_1}{v_2}}~r_1$
$r_2 = (\sqrt{\frac{0.62~m/s}{2.50~m/s}})~(1.1~cm)$
$r_2 = 0.55~cm$
Since the radius is half the diameter, the diameter of the water flow after the water has fallen 30 cm is $1.1~cm$.
