Question

The ceiling of a hall is $40m$ high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed $56m/s$ without hitting the ceiling is?

Answer 1

V² sin² Ф - 2 g H = 0² => V² sin² Ф = 2 g H => 56 * 56 sin² Ф = 2 * 9.8 * 40

Sin² Ф = 1/4 => sin Ф = 1/2 => 30 degrees

Maximum height = H Range = R angle of projection = Ф

H / R = (1/4 ) tan Ф

H = 40 m

tan Ф = 1/√3

Maximum range = R = 160 √3 m at this angle 30 deg