For anti-ballistic missile system, the time of flight tf is determined by the initial speed v0 of the missile and the maximum range r of the incoming missile. find their relationship.

Refer to the diagram shown below.

The following discussion assumes a simplistic analysis that ignores air resistance and variations in the terrain that the missile travels over.

Let the launch velocity be V₀ at an angle of θ relative to the horizontal.
The horizontal component of velocity is V₀ cosθ.
If the time of flight is , then

where r = the range of the missile.

Also, the time, t, when the missile is at ground level is given by

where g = acceleration due to gravity.

t = 0 corresponds to when the missile is launched. Therefore


Therefore


Typically, θ=45° to achieve maximum range, so that


This analysis is more applicable to a scud missile rather than a powered, guided missile.


Usually, θ=45°