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Home » The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball is thrown with a speed of 40 ms^{-1}ms −1 can go without hitting the ceiling of the hall?
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball is thrown with a speed of 40 ms^{-1}ms −1 can go without hitting the ceiling of the hall?
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball is thrown with a speed of 40 ms^{-1}ms −1 can go without hitting the ceiling of the hall?

Answer :

According to the question, the speed of the ball is u = 40 ms-1

And the maximum height is h = 25 m

The maximum height obtained by a body projected at an angle θ in projectile motion is given as:

h=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}

25=\frac{{{40}^{2}}{{\sin }^{2}}\theta }{2\times 9.8}

{{\sin }^{2}}\theta =0.30625

\sin \theta =0.5534

\therefore \theta ={{33.60}^{\circ }}

Horizontal range can be found in following manner :

R=\frac{{{u}^{2}}\sin 2\theta }{g}

R=\frac{{{40}^{2}}\times \sin 2(33.60)}{9.8}

R=\frac{1600\times 0.922}{9.8}

R=150.53m

i

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