Solution to a similar problem has been posted earlier which please check.
B) The total mechanical energy = KE + PE of the object at the surface of Eris will remain constant and will be equal to PE at the max. height h (above the surface). The object's KE will be zero at the max. ht. attained.
Eris, the largest dwarf planet known in the Solar System, has a radius R = 1200 km and an acceleration due to gravity on its surface of magnitude g = 0.77 m/s2.
(a) Use these numbers to calculate the escape speed from the surface of Eris.
(b) If an object is fired directly upward from the surface of Eris with one fourth of this escape speed, to what maximum height above the surface will the object rise? (Assume that Eris has no atmosphere and negligible rotation.)
I know the answer to a) is 1360 m/s, but I cannot figure out b). I know I should be using the conversation equation. However, I don't know how to apply it.
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