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A projectile motion with drag can be computed generically by numerical integration of the ordinary differential equation, for instance by applying a reduction to a first-order system. The equation to be solved is
Ideal projectile motion states that there is no air resistance and no change in gravitational acceleration.This assumption simplifies the mathematics greatly, and is a close approximation of actual projectile motion in cases where the distances travelled are small.
Assume the motion of the projectile is being measured from a free fall frame which happens to be at (x,y) = (0,0) at t = 0. The equation of motion of the projectile in this frame (by the equivalence principle) would be = ().
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
In projectile motion the most important force applied to the ‘projectile’ is the propelling force, in this case the propelling forces are the muscles that act upon the ball to make it move, and the stronger the force applied, the more propelling force, which means the projectile (the ball) will travel farther. See pitching, bowling.
A projectile following a ballistic trajectory has both forward and vertical motion. Forward motion is slowed due to air resistance, and in point mass modeling the vertical motion is dependent on a combination of the elevation angle and gravity. Initially, the projectile is rising with respect to the line of sight or the horizontal sighting plane.
Newton's cannonball is a thought experiment that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward ...
A projectile is any object projected into space (empty or not) by the exertion of a force. Although any object in motion through space (for example a thrown baseball) is a projectile, the term most commonly refers to a weapon. [8] [9] Mathematical equations of motion are used to analyze projectile trajectory. [citation needed]
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