A catapult is tested by Roman legionnaires. They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units) : Range = 0.3 km; angle of launch = π/6 rad; landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible?

v₀ = 50.46 m / s

Explanation:

This is a projectile launch exercise where the scope is given by

R = v₀² sin 2 θ / g

Let's clear the initial speed

v₀ = √ (G R / sin 2θ)

Let's reduce the distance

R = 0.3 km (1000m / 1km)

R = 300 m

Let's calculate

v₀ = √ (9.8 300 / sin2 π / 6)

Let's calculate the breast in radians

sin π / 3 = 0.8660

v₀ = √ (2546.11)

v₀ = 50.46 m / s