Given the earth\'s Radius, R(= 6.38*10^6m, mass of earth =5.97*10^24kg,and the g

Question

Given the earth's Radius, R(= 6.38*10^6m, mass of earth =5.97*10^24kg,and the gravational constant G=6.67*10^-11 Nm^2/Kg^2.A mass of 10^5 kg is now shot up vertically with velocity V and reaches a height of R(earth) above the ground.

what is the minimum velocity???

Given the earth's Radius, R(= 6.38*10^6m, mass of earth =5.97*10^24kg,and the gravational constant G=6.67*10^-11 Nm^2/Kg^2.A mass of 10^5 kg is now shot up vertically with velocity V and reaches a height of R(earth) above the ground. what is the minimum velocity???

Explanation / Answer

initial mechanical energy = final mechanical enrgy

-G*M*m/Re + 0.5*m*v^2 = -G*M*m/(2*Re)


0.5*m*v^2 = G*M*m/Re - G*M*m/(2*Re)

0.5*m*v^2 = 0.5*G*M*m/Re

v = sqrt(G*M/Re)

= sqrt(G*M/Re^2)*sqrt(Re)

= sqrt(g)*sqrt(Re)

= sqrt(9.8)*sqrt(6.38*10^6)

= 7.9*10^3 m/s

= 7.9 km/s

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