The answer is c.
Hope this helps!!!!!!!!!!
Grav. Potential at surface of the asteroid:
V = - G.Ma./ R
V = (-) 6.67^-11 x 4.0^20kg / 5.7^5m .. .. V = (-) 4.681 *10 ^5 J/kg
The GPE of the package on the asteroid = 9.0kg x (-) 4.681*10^5J/kg = (-) 4.21 ^5
J
This is the amount of energy required to come back the
package to infinity.
The total energy that needs to be transported to the package:
GPE + KE(for 187m/s)
Total energy required E = 4.21*10^5 + (½x 9.0kg x 168²) = 5.48 * 10^5 J
When the required energy is to be complete by releasing a compressed spring,
Elastic PE stored in spring = ½.ke² = 5.48 * 10^5 J where e = compression
distance
e = √ (2 x 5.48*10^5 / 2.1*10^5)
e = 2.28 m
