Q:
# What Are Catapult Launch Angle Equations?

**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.

Learn more about Calculus-
Q:
## How Did Leonard Euler Contribute to Mathematics?

A: Leonard Euler largerly contributed to the field of mathematics by proving existing theorems, finding the solutions to complex problems, introducing mathema... Full Answer >Filed Under: -
Q:
## What Is Cot X Equal To?

A: "Cot" is the abbreviation for "cotangent," a trigonometric function used to find the value of an angle in a right triangle by dividing the length of an adj... Full Answer >Filed Under: -
Q:
## How Do You Find the Value of Arctan 0?

A: Arctan, like arcsin and arccos, is an inverse trignometric function that determines at what angle a given fraction occurs. Inverse trigonometric functions ... Full Answer >Filed Under: -
Q:
## What Is the Definition of "sine?"

A: In math, the sine of an angle is defined as the length of the side of a right triangle opposite the acute angle divided by the length of the hypotenuse. Th... Full Answer >Filed Under: