Given: Suppose you are on a planet similar to Earth but where the acceleration o

Question

Given: Suppose you are on a planet similar to Earth but where the acceleration of gravity at the planet's surface is g = 10.9 m/s2 . Caution: The radius of this planet is the same as that of Earth's radius, but the mass may be different. Consider the case where the rocket is fired vertically to rise to a maximum height h = 5 R, the same relative height as in Part 1; i.e., r = R + h = 6R. Assume: All the rocket fuel is expended at the initial instant of firing; e.g., as in the case of a rail gun. Caution: Here you must take into account that the gravitational force is being reduced as the rocket moves upward into outer space. Find the initial velocity, immediately after it is fired. Answer in units of m/s

Explanation / Answer

so conservation of energy

Ei = Ef

- G M m/R + 1/2 m v^2= - G M m/(6R)

we are told that G M/R^2 = 10.9

so

-10.9 R + 0.5*v^2 = -10.9/6*R

-10.9*6.378E6 + 0.5*v^2 = -10.9/6*6.378E6

v = 10764 m/s

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