Question

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

Answer 1

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))