A sphere $1$ ft in diameter is moving horizontally at a depth of $12$ ft below a lake surface where the water temperature is $50F.$ Relative to the sphere, the maximum water speed is $V_{\text{m}\text{a}\text{x}}=1\mathrm{.}5-V_0.$ Here, $V_{\text{m}\text{a}\text{x}}$ occurs near the upper and lower parts of the sphere. The term $V_0$ is the speed of the sphere. At what sphere speed will cavitation first occur?