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Question
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?
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)`
sin2 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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