if they are colliding halfway up a cliff, then both objects travel 90m, therefore, if the ball is dropped, it will take, where:

s = 1/2 at^2

90 = 0.5 x 10 x t^2

t = 4.24 seconds

then, using this benchmark and appreciating the time taken for the stone fired upwards to be 4.24 to reach 90m up, either the stone has gone higher, and is already on its way down, or it is merely near the peak of its flight path

from there, if the stone travels 90m, use this formula:

s = vt - 1/2 at^2

90 = 4.24v - 0.5 x 10 x 4.24^2

90 = 4.24v - 90

180 = 4.24v

v = 42.45 m/s

stone would be fired at 42.45m/s