Acatapult 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

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14