#Projectile motion physics calculator full

The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target.

#Projectile motion physics calculator full

No exact solution is known that describes the full physical event under such an exerted resistance force.

Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction.The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. The range and the maximum height of the projectile does not depend upon its mass.

This equation will give the total time t the projectile must travel for to reach the target's horizontal displacement, neglecting air resistance. Since there is only acceleration in the vertical direction, the velocity in the horizontal direction is constant, being equal to v 0 cos ⁡ θ In this article a homogeneous acceleration is assumed. At higher speeds the trajectory can also be circular, parabolic or hyperbolic (unless distorted by other objects like the Moon or the Sun).

However, if an object was thrown and the Earth was suddenly replaced with a black hole of equal mass, it would become obvious that the ballistic trajectory is part of an elliptic orbit around that black hole, and not a parabola that extends to infinity. This causes an elliptic trajectory, which is very close to a parabola on a small scale. On Earth the acceleration changes magnitude with altitude and direction with latitude/longitude. The horizontal and vertical components of a projectile's velocity are independent of each other.Ī ballistic trajectory is a parabola with homogeneous acceleration, such as in a space ship with constant acceleration in absence of other forces. This is the principle of compound motion established by Galileo in 1638, and used by him to prove the parabolic form of projectile motion. In projectile motion, the horizontal motion and the vertical motion are independent of each other that is, neither motion affects the other.

5 Projectile motion on a planetary scale.

3.2 Trajectory of a projectile with Newton drag.

3.1 Trajectory of a projectile with Stokes drag.

3 Trajectory of a projectile with air resistance.

2.9 Total Path Length of the Trajectory.

2.8 Angle θ required to hit coordinate (x, y).

2.6 Application of the work energy theorem.

2.4 Relation between horizontal range and maximum height.

2.2 Time of flight to the target's position.

2.1 Time of flight or total time of the whole journey.

A ballistic missile is a missile only guided during the relatively brief initial powered phase of flight, and whose remaining course is governed by the laws of classical mechanics.īallistics (from Ancient Greek βάλλειν bállein 'to throw') is the science of dynamics that deals with the flight, behavior and effects of projectiles, especially bullets, unguided bombs, rockets, or the like the science or art of designing and accelerating projectiles so as to achieve a desired performance. Taking other forces into account, such as aerodynamic drag or internal propulsion (such as in a rocket), requires additional analysis. Because of the object's inertia, no external force is needed to maintain the horizontal velocity component of the object's motion. The only force of mathematical significance that is actively exerted on the object is gravity, which acts downward, thus imparting to the object a downward acceleration towards the Earth’s center of mass. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. This curved path was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upwards. Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected near Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are passive and assumed to be negligible). Components of initial velocity of parabolic throwing