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A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
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 physics, a projectile launched with specific initial conditions will have a range. It may be more predictable assuming a flat Earth with a uniform gravity field, and no air resistance. The horizontal ranges of a projectile are equal for two complementary angles of projection with the same velocity.
This article needs attention from an expert in Physics. The specific problem is: ... Angle of elevation (φ) at the maximum height is given by:
The terminal velocity depends on many factors including mass, drag coefficient, and relative surface area and will only be achieved if the fall is from sufficient altitude. A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft).
The blue path in this image is an example of a hyperbolic trajectory. A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red.
The pressure (force per unit area) at a given altitude is a result of the weight of the overlying atmosphere. If at a height of z the atmosphere has density ρ and pressure P , then moving upwards an infinitesimally small height dz will decrease the pressure by amount dP , equal to the weight of a layer of atmosphere of thickness dz .
The max q, or maximum dynamic pressure, condition is the point when an aerospace vehicle's atmospheric flight reaches the maximum difference between the fluid dynamics total pressure and the ambient static pressure. For an airplane, this occurs at the maximum speed at minimum altitude corner of the flight envelope.