$\displaystyle \Delta y = v_0\sin{\theta} \cdot t - \frac{g}{2} t^2$
$\displaystyle t = \frac{\Delta x}{v_0 \cos{\theta}}$
sub for $\displaystyle t$ ...
$\displaystyle \Delta y = \Delta x \tan{\theta} - \frac{g}{2} \cdot \frac{(\Delta x)^2 \sec^2{\theta}}{v_0^2} > h$
where $\displaystyle h$ is the height of the crossbar.