# Answer to Question #21164 in Mechanics | Relativity for beeta

Question #21164

a rocket is launched with velocity 10km/s.if radius of earth is R ,what will be the maximum height attained by it ?

Expert's answer

T+U=const

T - kinetic energy

U - potential energy

v0=10 km/s

mv0^2/2+Gamma*m*M/R=Gamma*m*M/(R+hmax)

M - mass of Earth

R+hmax = Gamma*M/(Gamma*M/R+v0^2/2)

hmax=R/(1+Rv0^2/(2Gamma*M)) - R =R/(1+2Gamma*M/(v0^2*R))

Answer: hmax=R/(1+2Gamma*M/(v0^2*R))

T - kinetic energy

U - potential energy

v0=10 km/s

mv0^2/2+Gamma*m*M/R=Gamma*m*M/(R+hmax)

M - mass of Earth

R+hmax = Gamma*M/(Gamma*M/R+v0^2/2)

hmax=R/(1+Rv0^2/(2Gamma*M)) - R =R/(1+2Gamma*M/(v0^2*R))

Answer: hmax=R/(1+2Gamma*M/(v0^2*R))

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