Pluto, the second largest dwarf planet in the Solar System, has a radius R = 114
ID: 1982987 • Letter: P
Question
Pluto, the second largest dwarf planet in the Solar System, has a radius R = 1140 km and an acceleration due to gravity on its surface of magnitude g = 0.66 m/s2.a) Use these numbers to calculate the escape speed from the surface of Pluto.
Answer=1226.70 m/s
b) If an object is fired directly upward from the surface of Pluto with half of this escape speed, to what maximum height above the surface will the object rise? (Assume that Pluto has no atmosphere and negligible rotation.)
I got a (v=1226.70), but I'm struggling with b. I tried (1/2)mv^2=mgh, but that wasn't right. I appreciate any help.
Explanation / Answer
Escape velocity V = 1226.7 m / s
Initial velocity of the object v = V / 2
= 613.35 m / s
Radius R = 1140000 m
Total energy on the surface = Total energy at top
( 1/ 2) mv 2 + [-GMm/ R ] = [-GMm/(R+h)]
( 1/ 2) v 2 + [-GM/ R ] = [-GM/(R+h)]
Where M = Mass of pluto
= 1.3 x 10 22 kg
G = Gravitational constant
= 6.67 x 10 -11 Nm 2/ kg 2
Substitute values we get 188099.11 -(760.61 x 10 3 ) = -(8.671 x 10 11 ) /(R+h)
-(8.671 x 10 11 ) /(R+h) = -572510.89
R + h = 1.514 x 10 6 m
Required height h = 374.556 x 10 3 m