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^-1 can go without hitting the ceiling of the hall?

Given:

Height of the hall= H = 25m

Velocity of the ball = Velocity of the projectile = v = 40 m/s

By applying the concept of projectile motion, we know that

ϕ= Angle that the projectile makes with the horizontal

g= Acceleration due to gravity= 9.8 m/s²

Sin ϕ = 0.5533

⇒ ϕ = sin^-1(0.5533)

⇒ ϕ = 33.6˚

R = Range of the projectile (or) horizontal distance travelled by the projectile.

= m

= 150.5m

Therefore, the ball can cover a maximum distance of 150.5m without hitting the ceiling of the wall.