# Projection from elevation (height, distance, duration) Calculator

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

 Initial height becomes negative if it is lower than landing point which is zero meter.
Initial velocity vs
 m/s km/h fps mph
Initial angle θs
 degree, 0≦θ≦90
Initial height h0
 m ft
[ Gravity g
 m/s2 ]

Flight duration t
 sec
Maximum height h
Travel distance l
Landing velocity ve
=
Landing angle θe
 degree
 $\normal Projection\ from\ elevation\\(1)\ h=h_0+{\large\frac{\left(v_s\sin\theta_s \right)^2}{2g}}\\(2)\ v_e=\sqrt{\left(v_s\cos\theta_s\right)^2 + 2gh}\\(3)\ \theta_e=\tan^{\tiny -1}\left({\large\frac{\sqrt{2gh}}{v_s\hspace1\cos\theta_s}}\right)\\(4)\ l={\large\frac{{v_s}^2\sin2\theta_s +{v_e}^2\sin2\theta_e}{2g}}\\$

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