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In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s), [citation needed] which is almost the terminal velocity of the peregrine falcon diving down on its prey. [4] The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to earth having been fired upwards, or ...
d is the total horizontal distance travelled by the projectile. 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; y 0 is the initial height of the projectile
The range and the maximum height of the projectile do not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height (=).
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.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
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 ...
is the distance of the orbiting body from the central body, is the length of the semi-major axis, is the standard gravitational parameter. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem to find:
Settling velocity W s of a sand grain (diameter d, density 2650 kg/m 3) in water at 20 °C, computed with the formula of Soulsby (1997). When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero.