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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.
We are interested in the time when the projectile returns to the same height it originated. Let t g be any time when the height of the projectile is equal to its initial value. 0 = v t sin θ − 1 2 g t 2 {\displaystyle 0=vt\sin \theta -{\frac {1}{2}}gt^{2}}
Maximum height of projectile. The greatest height that the object will reach is known as the peak of the object's motion. The increase in height will last until =, that is, = (). Time to reach the maximum height(h):
Using this formula the height of the tree can be calculated no matter what angle you are holding your arm, and no matter what the length of the yardstick that extends above your hand. This has a big advantage if you are measuring a tree on uneven ground or if you can only measure the tree from a single angle.
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 ...
The Arakelov height on a projective space over the field of algebraic numbers is a global height function with local contributions coming from Fubini–Study metrics on the Archimedean fields and the usual metric on the non-Archimedean fields. [15] [16] It is the usual Weil height equipped with a different metric. [17]
Unlike other methods of measuring the speed of a bullet, the basic calculations for a ballistic pendulum do not require any measurement of time, but rely only on measures of mass and distance. [ 1 ] In addition its primary uses of measuring the velocity of a projectile or the recoil of a gun, the ballistic pendulum can be used to measure any ...
Pace [6] in minutes per kilometre or mile vs. slope angle resulting from Naismith's rule [7] for basal speeds of 5 and 4 km / h. [n 1]The original Naismith's rule from 1892 says that one should allow one hour per three miles on the map and an additional hour per 2000 feet of ascent.