The shell has horizontal position [tex]x[/tex] and vertical position [tex]y[/tex] at time [tex]t[/tex] according to
[tex]x=\left(310\dfrac{\rm m}{\rm s}\right)\cos50.0^\circ t[/tex]
[tex]y=\left(310\dfrac{\rm m}{\rm s}\right)\sin50.0^\circ t-\dfrac g2t^2[/tex]
where [tex]g=9.80\dfrac{\rm m}{\mathrm s^2}[/tex] is the acceleration due to gravity.
The shell explodes after 39.0 s, at which point its coordinates are
[tex]x=7770\,\mathrm m[/tex]
[tex]y=1810\,\mathrm m[/tex]
