A missile starts from rest at ground level, travels along a straight line under

Question

A missile starts from rest at ground level,
travels along a straight line under the influ-
ence of rockets to attain a speed v0 quickly,
and then follows the normal path of a projec-
tile only under the influence of gravity with-
out rockets. The attainment of v0 happens
in a short distance compared to the missile’s
range. The missile is aimed optimally.
For the intercontinental ballistic missile to
have a range of 15000 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

Explanation / Answer

we know maximum range of projectile is at 45 degree
hence speed of missile in y direction = vo/2

time of flight = 2*(vo/(g*2)) ; where g is gravity constant

now 15000000meter = time*speed = 2*(vo/(g*2)) *vo/2 = vo2/g

v0 = 12.124km/s

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