“projectile”的概念、定义、翻译、参考文献-科学参考

projectile

Physics

Any body that is thrown or projected. If the projectile is discharged on the surface of the earth at an angle θ‎ to the horizontal it will describe a parabolic flight path (if θ‎ < 90° and the initial velocity < the escape velocity). Neglecting air resistance, the maximum height of this flight path will be (v²sin²θ‎)/2g, where v is the velocity of discharge and g is the acceleration of free fall. The horizontal distance covered will be (v²sin2θ‎)/g and the time of the flight will be (2vsinθ‎)/g. This means that, if air resistance is neglected, the launch angle needed for the furthest possible horizontal distance is 45°.

Mathematics

When a small body is travelling near the Earth’s surface, subject to no forces except the uniform gravitational force and possibly air resistance, it may be called a projectile. The standard mathematical model uses a particle to represent the body and a horizontal plane to represent the Earth’s surface.

When there is no air resistance, the trajectory, the path traced out by the projectile, is a parabola whose vertex corresponds to the point at which the projectile attains its maximum height. Take the origin at the point of projection, the x-axis horizontal and the y-axis vertical with the positive direction upwards. Then the equation of motion is $m \ddot{r} = - m g j$ , subject to r = 0 and $\dot{r} = (v cos θ) i + (v sin θ) j$ at t = 0, where v is the speed of projection and θ‎ is the angle of projection. This gives

$x = (v cos θ) t and y = (v sin θ) t - \frac{1}{2} g t^{2},$

for t ≥ 0. It follows that y = 0 when t = (2v/g)sinθ‎, the time of flight, and x = (v²/g)sinθ‎, the range of the projectile.

The maximum height of v²sin²θ‎/(2g) is attained halfway through the flight. The maximum range, for any given value of v, is obtained when θ‎=π‎/4. Similar investigations can be carried out for a projectile projected from a point a given height above a horizontal plane or projected up or down an inclined plane. For a body projected vertically upwards with initial speed v, set θ‎ = π‎/2.

Space Exploration

A particle that travels with both horizontal and vertical motion in the Earth's gravitational field. If the frictional forces of air resistance are ignored, the two components of its motion can be analysed separately: its vertical motion will be accelerated due to its weight in the gravitational field; its horizontal motion may be assumed to be at constant velocity. In a uniform gravitational field and in the absence of frictional forces the path of a projectile is a parabola.

单词	projectile
释义	projectile Physics Any body that is thrown or projected. If the projectile is discharged on the surface of the earth at an angle θ‎ to the horizontal it will describe a parabolic flight path (if θ‎ < 90° and the initial velocity < the escape velocity). Neglecting air resistance, the maximum height of this flight path will be (v²sin²θ‎)/2g, where v is the velocity of discharge and g is the acceleration of free fall. The horizontal distance covered will be (v²sin2θ‎)/g and the time of the flight will be (2vsinθ‎)/g. This means that, if air resistance is neglected, the launch angle needed for the furthest possible horizontal distance is 45°. Mathematics When a small body is travelling near the Earth’s surface, subject to no forces except the uniform gravitational force and possibly air resistance, it may be called a projectile. The standard mathematical model uses a particle to represent the body and a horizontal plane to represent the Earth’s surface. When there is no air resistance, the trajectory, the path traced out by the projectile, is a parabola whose vertex corresponds to the point at which the projectile attains its maximum height. Take the origin at the point of projection, the x-axis horizontal and the y-axis vertical with the positive direction upwards. Then the equation of motion is $m \ddot{r} = - m g j$ , subject to r = 0 and $\dot{r} = (v cos θ) i + (v sin θ) j$ at t = 0, where v is the speed of projection and θ‎ is the angle of projection. This gives $x = (v cos θ) t and y = (v sin θ) t - \frac{1}{2} g t^{2},$ for t ≥ 0. It follows that y = 0 when t = (2v/g)sinθ‎, the time of flight, and x = (v²/g)sinθ‎, the range of the projectile. The maximum height of v²sin²θ‎/(2g) is attained halfway through the flight. The maximum range, for any given value of v, is obtained when θ‎=π‎/4. Similar investigations can be carried out for a projectile projected from a point a given height above a horizontal plane or projected up or down an inclined plane. For a body projected vertically upwards with initial speed v, set θ‎ = π‎/2. Space Exploration A particle that travels with both horizontal and vertical motion in the Earth's gravitational field. If the frictional forces of air resistance are ignored, the two components of its motion can be analysed separately: its vertical motion will be accelerated due to its weight in the gravitational field; its horizontal motion may be assumed to be at constant velocity. In a uniform gravitational field and in the absence of frictional forces the path of a projectile is a parabola.
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