Question
A rocket is fired straight up through the atmosphere from the South Pole, burning out at an altitude of 208 km when traveling at 5.8 km/s.
(a) What maximum distance from Earth's surface does it travel before falling back to Earth?
(a) What maximum distance from Earth's surface does it travel before falling back to Earth?
Answers
drwls
The Earth's radius is Re = 6378 km.
Burnout occurs when R = 6586 km.
At the highest altitude, the burnout kinetic energy equals the gain in potential energy.
(1/2) M V^2 = GM[1/R - 1/(R+h)]
Solve for R+h. R+h-Re is the distance from the surface of the earth.
M is the Earth's mass and G is the universal constant of gravity.
In case you don't want to look up M and G,you can use the fact that
GM/Re^2 = g = 9.81 m/s^2
Burnout occurs when R = 6586 km.
At the highest altitude, the burnout kinetic energy equals the gain in potential energy.
(1/2) M V^2 = GM[1/R - 1/(R+h)]
Solve for R+h. R+h-Re is the distance from the surface of the earth.
M is the Earth's mass and G is the universal constant of gravity.
In case you don't want to look up M and G,you can use the fact that
GM/Re^2 = g = 9.81 m/s^2