For anti-ballistic missile system, the time of flight tf is determined by the initial speed v0 of the missile and the maximum ra

Question

Alex787

2 months ago

6

For anti-ballistic missile system, the time of flight tf is determined by the initial speed v0 of the missile and the maximum ra

nge r of the incoming missile. find their relationship.

Physics

1 answer:

Ostrovityanka [3.2K] · Answer 1 · 2026-03-07T23:26:10+03:00

Refer to the diagram below.

This discussion operates under a basic analysis that overlooks air resistance and variations in the terrain the missile traverses.

Let V₀ be the launch velocity, at an angle θ to the horizontal.
The horizontal velocity component equals V₀ cosθ.
If the flight duration is $t_{f}$ , then
$r=V_{o} \, t_{f}$
where r represents the missile's range.

The time t at which the missile is at ground level is expressed by
$0=V_{o} sin\theta \, t- \frac{1}{2}gt^{2}$
where g signifies acceleration due to gravity.

t = 0 signifies the missile's launch. Thus
$t_{f} = \frac{2V_{o}sin\theta}{g}$

Consequently,
$r= \frac{2V_{o}^{2} sin\theta cos\theta}{g} = \frac{V_{o}^{2} sin(2\theta)}{g}$

Typically, an angle of θ=45° is optimal for achieving maximum range, resulting in
$r= \frac{V_{o}^{2}}{g}$

This discussion applies more accurately to a scud missile than to a powered, guided missile.

Response:
$t_{f} = \frac{r}{V_{o} cos\theta} \\\\ r= \frac{V_{o}^{2} sin(2\theta)}{g}$
Usually, θ=45°