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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.
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
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 (=).
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers.
This is due to the nature of right triangles. Additionally, from the equation for the range : = We can see that the range will be maximum when the value of is the highest (i.e. when it is equal to 1).
These equations can be derived from the normal form of the line equation by setting = , and = , and then applying the angle difference identity for sine or cosine. These equations can also be proven geometrically by applying right triangle definitions of sine and cosine to the right triangle that has a point of the line and the origin as ...
The metacentric height (GM) is a measurement of the initial static stability of a floating body. [1] It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger metacentric height implies greater initial stability against overturning.
Suppose that f is differentiable at (,), with derivative K, and assume without loss of generality that >, so the tangent line at has positive slope (is increasing). Then there is a neighborhood of x 0 {\displaystyle x_{0}} on which the secant lines through x 0 {\displaystyle x_{0}} all have positive slope, and thus to the right of x 0 ...