Projectile motion

ballistic trajectorylofted trajectoryballistictrajectoryTrajectory of a projectileballistic trajectoriesangular ballistic trajectoryballistic arcballistic descentballistically
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).wikipedia
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Galileo Galilei

GalileoGalileanGalilei
This curved path was shown by Galileo to be a parabola.
Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and "hydrostatic balances", inventing the thermoscope and various military compasses, and using the telescope for scientific observations of celestial objects.

Ballistics

ballisticforensic ballisticsballistically
The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory.
After millennia of empirical development, the discipline of ballistics was initially studied and developed by Italian mathematician Niccolò Tartaglia in 1531, although he continued to use segments of straight-line motion, conventions established by Avicenna and Albert of Saxony, but with the innovation that he connected the straight lines by a circular arc. Galileo established the principle of compound motion in 1638, using the principle to derive the parabolic form of the ballistic trajectory.

Motion

movementMotion (physics)locomotion
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).

Projectile

projectileskinetic kill vehiclekinetic projectile
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).

Gravity

gravitationgravitationalgravitational force
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).

Parabola

parabolicparabolic curveparabolic arc
This curved path was shown by Galileo to be a parabola.

Acceleration

decelerationacceleratem/s 2
The only force of significance that acts on the object is gravity, which acts downward, thus imparting to the object a downward acceleration.

Inertia

inertialinertia forceinertial forces
Because of the object's inertia, no external horizontal force is needed to maintain the horizontal velocity component of the object.

Euclidean vector

vectorvectorsvector addition
Because of the object's inertia, no external horizontal force is needed to maintain the horizontal velocity component of the object.

Friction

coefficient of frictionstatic frictionfriction coefficient
Taking other forces into account, such as friction from aerodynamic drag or internal propulsion such as in a rocket, requires additional analysis.

Drag (physics)

dragaerodynamic dragair resistance
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible). Taking other forces into account, such as friction from aerodynamic drag or internal propulsion such as in a rocket, requires additional analysis.

Rocket

rocketsrocketryrocket scientist
Taking other forces into account, such as friction from aerodynamic drag or internal propulsion such as in a rocket, requires additional analysis.

Closed-form expression

closed formclosed-formanalytical solution
Detailed mathematical solutions of practical problems typically do not have closed-form solutions, and therefore require numerical methods to address.

Numerical analysis

numerical methodsnumericalnumerical computation
Detailed mathematical solutions of practical problems typically do not have closed-form solutions, and therefore require numerical methods to address.

Velocity

velocitiesvelocity vectorlinear velocity
Let the projectile be launched with an initial velocity, which can be expressed as the sum of horizontal and vertical components as follows:

Ellipse

ellipticalellipticeccentricity
This causes an elliptic trajectory, which is very close to a parabola on a small scale.

Black hole

black holesblack-holeblack hole physics
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.

Orbit

orbitsorbital motionplanetary motion
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.

Hyperbola

hyperbolicrectangular hyperbolahyperbolas
At higher speeds the trajectory can also be circular, parabolic or hyperbolic (unless distorted by other objects like the Moon or the Sun).

Pythagorean theorem

Pythagoras' theoremPythagorasPythagoras's theorem
:.The magnitude of the velocity (under the Pythagorean theorem, also known as the triangle law):

Displacement (vector)

displacementdisplacement vectordisplacements
At any time t, the projectile's horizontal and vertical displacement are:

Work (physics)

workmechanical workwork-energy theorem
According to the work-energy theorem the vertical component of velocity is:

Reynolds number

ReynoldsReynolds numbersRe
In this section we will take air resistance to be in direct proportion to the velocity of the particle (i.e. ). This is only valid at Reynolds number below about 1000.

Viscosity

viscouskinematic viscositydynamic viscosity
In air, which has a kinematic viscosity around 0.15 cm 2 /s this means that the product of speed and diameter must be less than about 150 cm 2 /s which is obviously not usually the case.

Drag equation

aerodynamic dragfrontal areasquare of the car's speed
At higher values of speed times diameter (high Reynolds number) the force of air resistance is proportional to the square of the particle's velocity (see drag equation).