The most commonly used formulas for 2D motion with projectile are:
The initial velocity can be calculated using the formula v0 = √(v0x^2 + v0y^2), where v0x and v0y are the horizontal and vertical components of the initial velocity. The angle can be calculated using the formula θ = tan^-1 (v0y/v0x).
The acceleration due to gravity for 2D motion with projectile is a constant value of 9.8 m/s^2, directed downwards towards the earth.
These formulas are applicable for any projectile that follows a parabolic path, such as objects thrown, launched, or dropped. They may not be accurate for objects with air resistance or for projectiles in non-uniform gravitational fields.
These formulas are specifically designed for 2D motion with projectile, where the motion is restricted to a vertical and horizontal plane. For 3D motion with projectile, additional formulas and calculations are required to account for the motion in the third dimension.