ballistic missile physics question?

Question

1) For the ballistic missile aimed to achieve the maximum range of 1000 km, what is the maximum altitude reached in the trajectory in km.

2) For the intercontinental ballistic missile to have a range of 10,500 km, what must be the speed (v0) of the missile at the end of the acceleration phase? Take the distance of the acceleration phase, as negligible compared to the travel time. Answer in km/s.

Answer 1

I will ignore the curvature of the Earth and air resistance.
Since I don't know anything about the acceleration phase, I will look at apogee to impact. Under my assumption, apogee will occur at 500 km down range
I also know that in the ballistic phase, the speed at impact is equal in magnitude to the velocity gained by falling from apogee in the vertical, and equal to the horizontal velocity at the end of the acceleration phase. I will assume that acceleration occurs before the missile reaches the surface of the ground from the silo where it was launched, and that it exited the silo at an angle of 45 degrees with no telemetry modification during flight.

Then
500/3.6=v0*cos(45)*t where t is the flight time from apogee to impact, and v0 is the magnitude of velocity at impact.
and
0=v0*sin(45)-g*t
since v0*sin(45) is equal to
v0*cos(45)
500/3.6=g*t^2
or t^2=500/(3.6*g)
the total vertical fall then is
.5*g*t^2
so
.5*500/3.6 is the height


2) is the same set of equations since the assumptions are the same. The only difference is the range
t^2=5250/(3.6*g)
t=sqrt(5250/(3.6*g))
the speed attained will be related to
0=v0*sin(45)-g*t
v0=g*t/sin(45)
since sin(45)=sqrt(2)/2
and t=sqrt(5250/(3.6*g))
v0=sqrt(2*g*5250/3.6)
j

Answer 2

From what I see interior the difficulty as written, you haven't any longer have been given sufficient suggestions to choose for and answer. R would be in instruments of meters, so the respond ought to derive from the made of v0 and tf (m/s·s=m). There could be some consistent in front of v0·tf. The function could be interior the form of ok·v0·tf. ok could rely on the ratio between the velocities of the two missiles. each and every of the stuff previous to v0 interior the solutions you ought to choose for between reduces to three consistent. I see no thank you to choose for between the constants you're given.