the ceiling of a long hall is 25 m high.what is the maximum horizontal distance that a ball thrown

Since the ceiling of hall is 25 m high therefore the max. height attained by the ball will be 25m.

i.e. H = 25m, u = 40 m/s  [given]

we know, H  =  u²sin²θ / 2g

or, sin²θ = 2gH / u²   = 2 x 9.8 x 25 / ( 40 )²  = 0.30625

or, sin  θ = 0.5534

or, θ = 33.6 ^o

Therefore, R = u²sinθ / g  =  (40)²  sin 67.2^o /9.8

                                              =  150.5 m