A ball is dropped from rest from a height h. Neglecting air resistance and taking the acceleration due to gravity to be g, calculate how ling it takes to hit the floor in terms of g and h.

so i set up two equations of motion.

$\displaystyle F = \frac{d}{dt}(mv) = -mgj $

$\displaystyle -mgj = m\frac{d^2x}{dt^{2}} i + m \frac{d^{2}y}{d^{2}}j $

there is not motion in the x direction so

$\displaystyle \frac{d^2x}{dt^{2}} = 0 $

$\displaystyle \frac{d^{2}y}{d^{2}} = -g $

so integrating twice i get two equations

$\displaystyle x(t) = x_{1}t + x_{0} $

$\displaystyle y(t) = -\frac{1}{2}gt^{2} + y_{1}t + y_{0} $

not sure where to go from here, any help appreciated, how do i work out the constants on integration ? I know the ball is dropped from rest, so one of the constants will be 0?