How much must the spring be compressed? helppp

[ohheytai]

how much must the spring be compressed?!? helppp

A package of mass 9 kg sits at the equator of an airless asteroid of mass 3.0x10^20 kg and radius 2.1x 10^5 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 179 m/s. We have a large and powerful spring whose stiffness is 2.3x10^5 N/m. How much must we compress the spring?

i can't get this someone please help me this is my work
escape speed:
v = sqrt(2GM/R); Where:
G = 6.673 E-11 [m³ / (kg-s²)]; Gravitational Constant
M = 3.0 E+20 kg; Mass of asteroid
R = 2.1 E+5 m; Radius of asteroid

v = sqrt[ 2 * 6.673 E10^(-11) [m³ / (kg-s²)] * 3.0 E10^20 kg ÷ (2.1 E10^5 m) ]
v = 1.9066 E5 m²/s²
v = 437 m/s


E = 1/2 m v²
E = 1/2 (9 kg) (437 m/s + 179 m/s)²
E = 4.5 kg (379496 m²/s²)
E = 1,707,500 J


E = 1/2 kx²
1.708 E6 kg m²/s² = 1/2 (2.3 E5 kg/s²) x²
14.85 m² = x²
x = 3.85m

 

[Redbelly98]

A package of mass 9 kg sits at the equator of an airless asteroid of mass 3.0x10^20 kg and radius 2.1x 10^5 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 179 m/s. We have a large and powerful spring whose stiffness is 2.3x10^5 N/m. How much must we compress the spring?

i can't get this someone please help me this is my work
escape speed:
v = sqrt(2GM/R); Where:
G = 6.673 E-11 [m³ / (kg-s²)]; Gravitational Constant
M = 3.0 E+20 kg; Mass of asteroid
R = 2.1 E+5 m; Radius of asteroid

v = sqrt[ 2 * 6.673 E10^(-11) [m³ / (kg-s²)] * 3.0 E10^20 kg ÷ (2.1 E10^5 m) ]
v = 1.9066 E5 m²/s²
v = 437 m/s


E = 1/2 m v²
E = 1/2 (9 kg) (437 m/s + 179 m/s)²

Your error starts here. It's incorrect to simply add the escape speed to the final desired speed.

E = 4.5 kg (379496 m²/s²)
E = 1,707,500 J


E = 1/2 kx²
1.708 E6 kg m²/s² = 1/2 (2.3 E5 kg/s²) x²
14.85 m² = x²
x = 3.85m

There are three forms of energy at play here: due to gravity, due to the spring, and kinetic energy. Using that, can you set up an equation from E_initial=E_final?