- #1
PsychonautQQ
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Homework Statement
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.
Homework 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.
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?