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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} ).
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} .
The path of this projectile launched from a height y 0 has a range d. ... The maximum horizontal distance travelled by the projectile, neglecting air resistance, ...
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.
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.
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The equations imply that the maximum height (H) ... Erlichson, Herman (1983). "Maximum projectile range with drag and lift, with particular application to golf".