the ceiling of a long hall is 25 m high . what is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall ?

the maximum possible height a projectile attains is given as

H = u²sin²θ / g

or the angle of projection will be given as

sinθ = [Hg / u²]^1/2

here,

H = 25m

u = 40 m/s

g = 10 m/s²

so,

sinθ = [(25x10) / 40²]^1/2

or

sinθ = 0.559

thus,

θ = 34 degree

now,

the maximum horizontal range will be

R = u²sin2θ / g

 = 40²sin(2x34) / 10

thus, we get

R = 148.3 m