1. The problem statement, all variables and given/known data A gun can fire an artillery shell with a speed v_0 in any direction. Show that a shell can strike any target within the surface given by: (gr)^2 = (v_0)^4 - (2gz)*(v_0)^2 where z is height and r is horizontal distance the target is from the gun. 2. Relevant equations Some useful equations that trivially derived: (v_0*cos(k))^2 = v_0^2 -2g*z_max z_max = ((v_0*sin(k))^2) / 2g. 3. The attempt at a solution I'm having problems getting anywhere near the answer. I tried playing around with the first term after substituting (r / (r^2+z^2)^1/2) for cos(k) ( can you even do this? the surface is an arc.) Anyone want to help guide me here?