__Question 4.15__:

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

^{2}Sin

^{2}θ / 2g

25 = (40)

^{2}Sin

^{2}θ / 2 X 9.8

sin

^{2 }

*θ*= 0.30625

sin

*θ*= 0.5534

∴

*θ*= sin

^{–1}(0.5534) = 33.60°

Horizontal range,

*R*= u

^{2}Sin 2

*θ / g*

= (40)

^{2}X Sin (2 X 33.60

^{0}) / 9.8

= 1600 X Sin (67.2) / 9.8

= 1600 X 0.922 / 9.8 = 150.53 m

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