For anti-ballistic missile system, the time of
flight tf is determined by the initial speed v0
of the missile and the range R.
What is the time (in minute) of the flight tf
available to kill an incoming intercontinental
ballistic missile launched from 10500 km away
with a speed of 8.8 km/s?
To calculate the time of flight (tf) of an anti-ballistic missile system, we need to know the initial speed (v0) of the missile and the range (R) between the missile and the target.
Given:
Initial speed (v0) = 8.8 km/s
Range (R) = 10,500 km
We can calculate the time of flight (tf) using the formula:
tf = R / v0
Substituting the given values into the formula:
tf = 10500 km / 8.8 km/s
To simplify the calculation, we convert the range from kilometers to meters:
tf = (10500 km * 1000 m/km) / 8.8 km/s
tf = 10500000 m / 8.8 km/s
Now, we need to convert the speed from km/s to m/s:
tf = 10500000 m / (8.8 km/s * 1000 m/km)
tf = 10500000 m / 8800 m/s
Now, we can calculate the time of flight (tf):
tf = 1193.18 seconds
Since the time is given in seconds, to convert it to minutes, we divide by 60:
tf = 1193.18 seconds / 60 seconds/minute
tf ≈ 19.89 minutes
Therefore, the time of flight (tf) available to kill the incoming intercontinental ballistic missile launched from 10,500 km away with a speed of 8.8 km/s is approximately 19.89 minutes.
To find the time of flight (tf) for an anti-ballistic missile system, we can use the formula:
tf = R / v0
Where:
- tf is the time of flight
- R is the range (distance) of the missile
- v0 is the initial speed of the missile
In this case, the intercontinental ballistic missile is launched from a distance of 10500 km (R = 10500 km) with a speed of 8.8 km/s (v0 = 8.8 km/s).
Using the formula, we can substitute the values:
tf = 10500 km / 8.8 km/s
We divide the range by the speed to get the time of flight. This is because the distance is divided by the velocity to obtain the time.
Now, let's calculate:
tf ≈ 1193.18 seconds
To convert seconds to minutes, we divide by 60:
tf ≈ 19.89 minutes
Therefore, the time of flight available to kill the incoming intercontinental ballistic missile launched from 10500 km away is approximately 19.89 minutes.
Assume you have the entire flight time of the ICBM available to make the kill. Make a flat earth, low trajectory approximation, with constant velocity of 8.8 km/s between launch and target.
The answer becomes simply 10,500/8.8 = 1193 s = 19.9 minutes.