After falling a distance of s body of mass m loses potential energy equalt to $\displaystyle m * g * h$

Gain in kinetic velocity $\displaystyle 1/2 m * v ^2

$

By law of conservation of evergy, loss in potential enrgy equals gain in kinetix energy

$\displaystyle => m * g * h = 1/2 m * v^2$

Which gives $\displaystyle v = sqrt (2 g * h)$

Hope you are looking for the same.

Also if you assume that mass has initial velocity, the just use change of kinetic energy equal to change in potential energy. So this will introduce the quantity initial velocity in the equation.