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 = u^{2}sin^{2}θ / g

or the angle of projection will be given as

sinθ = [Hg / u^{2}]^{1/2}

here,

H = 25m

u = 40 m/s

g = 10 m/s^{2}

so,

sinθ = [(25x10) / 40^{2}]^{1/2}

or

sinθ = 0.559

thus,

θ = 34 degree

now,

the maximum horizontal range will be

R = u^{2}sin2θ / g

= 40^{2}sin(2x34) / 10

thus, we get

**R = 148.3 m**

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