### Q.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 ?

**Answer:-**

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 × 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} × Sin (2 × 33.60^{0}) / 9.8

= 1600 × Sin (67.2) / 9.8

= 1600 × 0.922 / 9.8 = 150.53 m