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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 ( y = 0 {\textstyle y=0} ).
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
Maximum Height (): this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis (y-axis) covered by the projectile. It is given as H = U 2 sin 2 θ / 2 g {\displaystyle H=U^{2}\sin ^{2}\theta /2g} .
Maximum height can be calculated by absolute value of in standard form of parabola. It is given as H = | c | = u 2 2 g {\displaystyle H=|c|={\frac {u^{2}}{2g}}} Range ( R {\displaystyle R} ) of the projectile can be calculated by the value of latus rectum of the parabola given shooting to the same level.
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.
Projectile path values are determined by both the sight height, or the distance of the line of sight above the bore centerline, and the range at which the sights are zeroed, which in turn determines the elevation angle. A projectile following a ballistic trajectory has both forward and vertical motion.
Here, K and U denote the kinetic and potential energy of the ball, H is the maximum height of the ball, and T is the time of flight of the ball. The 'i' and 'f' subscript refer to the initial (before impact) and final (after impact) states of the ball. Likewise, the energy loss at impact can be related to the COR by
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 ...