The ceiling of a lone hall is 20 m high. What is the maximum horizontal distance that a ball thrown with…

Q: The ceiling of a lone hall is 20 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall (g = 10 ms2 ) ?

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Sol. Here, H = 20 m, u = 40 m/s

Suppose the ball is thrown at an angle θ with the horizontal.

$\large H = \frac{u^2 sin^2 \theta}{2 g} $

$\large 20 = \frac{(40)^2 sin^2 \theta}{2 \times 10} $

sinθ = 1/2 ⇒ θ = 30°

$\large R = \frac{u^2 sin2\theta}{g} $

$\large R = \frac{(40)^2 sin60^o}{10} $

= 138.56 m