Question

A ceiling of a long hall is 25 m high what is the horizontal maximum distance that a ball thrown with speed of 40 m/s can go without hitting the ceiling of wall.

Answer 1

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 = u2 Sin2θ / 2g
25 = (40)2 Sin2θ / 2 × 9.8
sin2 θ = 0.30625
sin θ = 0.5534
∴ θ = sin–1(0.5534) = 33.60°
Horizontal range, R = u2 Sin 2θ / g
= (40)2 × Sin (2 × 33.600) / 9.8
= 1600 × Sin (67.2) / 9.8
= 1600 × 0.922 / 9.8 = 150.53 m