# Answer to Question #4547 in Mechanics | Relativity for Lisa Thomas

Question #4547

For the intercontinental ballistic missile to have a range of 10000 km, what must be the speed v0 of the missile at the end of the acceleration phase? Take the distance of the acceleration phase, called the boost time, as negligible compared to the travel time. Answer in units of km/s

Expert's answer

θ - angle between initial velosity and horizon

for maximum range teta=45

Range R is given by

R = H component of velocity x time of flight

R = vo cos θ x 2 vo sin θ / g

R = 19500 x 10^3 m

sin 45 x cos 45 = 0.5

g = 9.81 m/s^2

vo^2 =R g / (2 x 0.5)

vo = 13831 m/s=13.8 km/s

for maximum range teta=45

Range R is given by

R = H component of velocity x time of flight

R = vo cos θ x 2 vo sin θ / g

R = 19500 x 10^3 m

sin 45 x cos 45 = 0.5

g = 9.81 m/s^2

vo^2 =R g / (2 x 0.5)

vo = 13831 m/s=13.8 km/s

**Answer: 13.8 km/s**
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