# Projection from elevation (velocity, angle, duration)

## Calculates the velocity, angle and duration of the projection from the initial and maximum height, and travel distance.

 Initial height becomes negative if it is lower than landing point which is zero meter.
Maximum height h
 m ft
Travel distance l
Initial height h0
[ Gravity g
 m/s2 ]

Initial velocity vs
=
Initial angle θs
 degree
Flight duration t
 sec
Landing velocity ve
=
Landing angle θe
 degree
 $\normal Projection\ from\ elevation\\\vspace{5}\\(1)\ t={\large \frac{\sqrt{2g(h-h_0)}+\sqrt{2gh}}{g}}\\(2)\ v_s=\sqrt{({\large\frac{l}{t})^2}+2g(h-h_0)}\\\hspace{25}\theta_s=\tan^{\tiny -1}\left({\large\frac{t\sqrt{2g(h-h_0)}}{l}}\right)\\(3)\ v_e=\sqrt{({\large\frac{l}{t}})^2+2gh}\\\hspace{25}\theta_e=\tan^{\tiny -1}\left({\large\frac{t\sqrt{2gh}}{l}}\right)$

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