sorry, the equations are :

eq3 := 6.767*(diff(z(t), t, t)) = -6.767*9.81-1.176*(.5*.6)*pi*0.65e-1^2*sqrt((diff(x(t), t))^2+(diff(z(t), t))^2)*(diff(z(t), t)) 

eq4 := 6.767*(diff(x(t), t, t)) = -1.176*(.5*.6)*pi*0.65e-1^2*sqrt((diff(x(t), t))^2+(diff(z(t), t))^2)*(diff(x(t), t))

b := dsolve([eq3, eq4, x(0) = 581.883877165126023, (D(x))(0) = 280.415752887592248, z(0) = 294.494520175761863, (D(z))(0) = 125.199003418353243], [x(t), z(t)], type = numeric) 

odeplot(b, [x(t), z(t)], 0 .. 3.59)