any time an object is "dropped" , its initial velocity is zero.

ball's position equation as a function of time ...

stone's position equation as a function of time ...

set the position equations equal since they have the same position ...

, where is the stone's initial velocity upward.

note the "no-time" equation for constant acceleration ...

at the top of its trajectory, the stone has zero velocity ...

sub in for in the equation ...

sub for in either position equation ...