Question

a stone is dropped from top of a tower of 50m high ,simltaneously another stone is thrown upward with a speed of 20m/s find the time when them cross each other

Answer 1

At the time that I'll call ' Q ', the height of the stone that was
dropped from the tower is

             H = 50 - (1/2 G Q²) ,

and the height of the stone that was tossed straight up
from the ground is

             H  =  20Q - (1/2 G Q²) .

The stones meet when them's heights are equal,
so that's the time when

                         50 - (1/2 G Q²)  =  20Q - (1/2 G Q²) .

This is looking like it's going to be easy.

Add  (1/2 G Q²)  to each side.
Then it says
                                             50  =  20Q

Divide each side by 20:          2.5  =  Q .

And there we are.  The stones pass each other

                                       2.5 seconds

after they are simultaneously launched.