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Projectile motion is a form of motion experienced by an ... target motion, acceleration due to gravity varying ... and with initial speed v, the required ...
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 ...
Given initial velocity u, one can calculate how high the ball will travel before it begins to fall. The acceleration is local acceleration of gravity g. While these quantities appear to be scalars, the direction of displacement, speed and acceleration is important. They could in fact be considered as unidirectional vectors.
To find the angle giving the maximum height for a given speed calculate the derivative of the maximum height = / with respect to , that is = / which is zero when = / =. So the maximum height H m a x = v 2 2 g {\displaystyle H_{\mathrm {max} }={v^{2} \over 2g}} is obtained when the projectile is fired straight up.
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.
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; y 0 is the initial height of the projectile; If y 0 is taken to be zero, meaning that the object is being launched on flat ground, the range of the projectile will simplify to:
In kinematics, ToF is the duration in which a projectile is traveling through the air. Given the initial velocity u {\displaystyle u} of a particle launched from the ground, the downward (i.e. gravitational) acceleration a {\displaystyle a} , and the projectile's angle of projection θ (measured relative to the horizontal), then a simple ...
As a gravitational force acts on the projectile, it will follow a different path depending on its initial velocity. If the speed is low, it will simply fall back on Earth. If the speed is the orbital speed at that altitude, it will go on circling around the Earth along a fixed circular orbit "and return to the mountain from which it was projected".