The horizontal and vertical positions, respectively, of the turd are
[tex]x=\left(19\dfrac{\rm m}{\rm s}\right)t[/tex]
[tex]y=64\,\mathrm m-\dfrac g2t^2[/tex]
where [tex]g=9.80\frac{\rm m}{\mathrm s^2}[/tex] is the acceleration due to gravity.
Solve [tex]y=0[/tex] for [tex]t[/tex] to find the time it takes for the turd to fall to the ground:
[tex]64\,\mathrm m-\dfrac g2t^2=0\implies t\approx13.06\,\mathrm s[/tex]
Substitute this into the equation for [tex]x[/tex] to find where the robot should stand:
[tex]x=\left(19\dfrac{\rm m}{\rm s}\right)(13\,\mathrm s)\approx248.16\,\mathrm m[/tex]
