Let both the particles meet after time, t .
Hence,
The distance covered by the particle coming down from the top of the tower, would be equal to:
s=12gt2......(1)
The distance covered by the particle going from ground would be given by:
h−s=ut−12gt2......(2)
From (1) and (2) the time taken by both to meet, would be given by:
t=hu
Hence, the time taken by both to meet is t=hu