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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?

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#### Solution

Speed of the ball, u = 40 m/s

Maximum height, h = 25 m

In projectile motion, the maximum height reached by a body projected at an angle θ, is given by the relation:

h = `(u^2sin^2theta)/(2g)`

25 = `((40)^2sin^2theta)/(2xx9.8)`

sin^{2 }θ = 0.30625

sin θ = 0.5534

∴θ = sin^{–1}(0.5534) = 33.60°

Horizontal range, R = `(u^2sin 2theta)/g`

= `((40)^2xxsin2xx33.60) /9.8`

= `(1600xxsin 67.2)/9.8`

= `(1600xx0.922)/9.8 = 150.53 "m"`

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