## College Physics (4th Edition)

The diameter of the water flow after the water has fallen 30 cm is $1.1~cm$
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 $1.1~cm$.