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Terminal velocity depends on atmospheric drag, the coefficient of drag for the object, the (instantaneous) velocity of the object, and the area presented to the airflow. Apart from the last formula, these formulas also assume that g negligibly varies with height during the fall (that is, they assume constant acceleration).
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
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.
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 (=).
The initial velocity, v i, ... To find the angle giving the maximum height for a given speed calculate the derivative of the maximum height = ...
The escape velocity at a given height is times the speed in a circular orbit at the same height, (compare this with the velocity equation in circular orbit). This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential ...
This provides a method to calculate the roughness length by measuring the friction velocity and the mean wind velocity (at known elevation) in a given, relatively flat location (under neutral conditions) using an anemometer. [4] Of note is that, in this simplified form, the log wind profile is identical in form to the dimensional law of the wall.
Given , the acceleration due to gravity, and , the final height of the pendulum, it is possible to calculate the initial velocity of the bullet-pendulum system using conservation of mechanical energy (kinetic energy + potential energy). Let this initial velocity be denoted by .