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The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
The omega equation is a culminating result in synoptic-scale meteorology.It is an elliptic partial differential equation, named because its left-hand side produces an estimate of vertical velocity, customarily [1] expressed by symbol , in a pressure coordinate measuring height the atmosphere.
In words, this equation says that as a vertical column of water is squashed, it moves toward the Equator; as it is stretched, it moves toward the pole. Assuming, as did Sverdrup, that there is a level below which motion ceases, the vorticity equation can be integrated from this level to the base of the Ekman surface layer to obtain:
Equation [3] involves the average velocity v + v 0 / 2 . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows ...
v is the velocity at which the projectile is launched g is the gravitational acceleration —usually taken to be 9.81 m/s 2 (32 f/s 2 ) near the Earth's surface θ is the angle at which the projectile is launched
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The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is: