floating object box
floating
$$\tag{1} \rho_2 = \left( 1 + \frac{h_1}{h_2} \right) \rho_1 $$
sinking $(h_1 = 0)$
$$\tag{2} \rho_2 \le \rho_1 $$
buoyant $(h_1 = 0)$
$$\tag{3} \rho_2 = \rho_1, \ \ \ \ v_y(0) = 0 $$
$$\tag{1} \rho_2 = \left( 1 + \frac{h_1}{h_2} \right) \rho_1 $$
$$\tag{2} \rho_2 \le \rho_1 $$
$$\tag{3} \rho_2 = \rho_1, \ \ \ \ v_y(0) = 0 $$