Launching angle equations are mathematical equations that predict the trajectory and the landing place of a projectile when launched from a catapult at a specific angle. These equations are necessary to accurately aim a catapult and have its projectile hit an intended target with precision.
Galileo developed the equations by hypothesizing that two forces affect a launched projectile. The law of gravity affects its vertical elevation. Under this law, any projectile in flight is pulled toward the earth at a rate of 9.8 meters per second. Inertia impacts the horizontal distance traveled. By calculating the two motions working together, he discovered that they create a precise mathematical curve. The geometric shape called a parabola demonstrates the curve.
Parabolas are symmetrical, so the path to the apex is a mirror of the path back to earth. This means that a projectile launched from a catapult at a 45-degree angle travels the farthest distance possible. If the object is launched at less than 45 degrees, it does not go as high, and gravity pulls it down to earth more quickly. If it launches at a greater angle than 45 degrees, it travels higher, but not as far, because there is less forward inertia. This symmetry means that a projectile launched at 60 degrees goes exactly the same distance as one launched at 30 degrees; they simply take different paths.