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.


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