Find Velocity with only range given.

[Jimkatz809]

Homework Statement

For the intercontinental ballistic missile to
have a range of 16000 km, what must be
the speed v0 of the missile at the end of the
accelaration phase? Take the distance of the
accelaration phase, called the boost time, as
negligible compared to the travel time.
Answer in units of km/s.

Homework Equations

The Attempt at a Solution

 

[lewando]

The problem needs another constraint, like maximum height or launch angle for it to have a singular v0 solution. Double check the problem statement, pick some relevant equations, and show us where you are getting stuck.

 

[tomcue]

To find the velocity, we can use the formula for range:

R = v0*t

Where R is the range, v0 is the initial velocity, and t is the time of flight.

Since the boost time is negligible compared to the travel time, we can assume that t is equal to the travel time.

Therefore, rearranging the formula, we get:

v0 = R/t

Substituting the given values, we get:

v0 = 16000 km / t

Since we do not have the exact value of t, we cannot determine the exact velocity. However, we can estimate the velocity by using the average travel time for an intercontinental ballistic missile, which is approximately 30 minutes or 1800 seconds.

Therefore, the estimated velocity would be:

v0 = 16000 km / 1800 s = 8.89 km/s

This is the approximate velocity at the end of the acceleration phase for the intercontinental ballistic missile with a range of 16000 km.