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θ is the angle at which the projectile is launched; y 0 is the initial height of the projectile; If y 0 is taken to be zero, meaning that the object is being launched on flat ground, the range of the projectile will simplify to: =
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.
The clinometer and tape method, or the tangent method, is commonly used in the forestry industry to measure log length. [15] [16] Some clinometers are hand held devices used to measure angles of slopes. The user can sight to the top of a tree using such a clinometer and read the angle to the top using a scale in the instrument.
This formula allows one to find the angle of launch needed without the restriction of =. One can also ask what launch angle allows the lowest possible launch velocity. This occurs when the two solutions above are equal, implying that the quantity under the square root sign is zero.
Jurin's law, or capillary rise, is the simplest analysis of capillary action—the induced motion of liquids in small channels [1] —and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter.
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]
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It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement). A longitudinal deformation (in the direction of the axis) is called elongation . The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of ...