Respuesta :
Answer:
c. [tex]4.582\times10^{21} kg[/tex]
Explanation:
[tex]r_{i}[/tex] = Initial distance between asteroid and rock = 7514 km = 7514000 m
[tex]r_{f}[/tex] = Final distance between asteroid and rock = 2823 km = 2823000 m
[tex]v_{i}[/tex] = Initial speed of rock = 136 ms⁻¹
[tex]v_{f}[/tex] = Final speed of rock = 392 ms⁻¹
[tex]m[/tex] = mass of the rock
[tex]M[/tex] = mass of the asteroid
Using conservation of energy
Initial Kinetic energy of rock + Initial gravitational potential energy = Final Kinetic energy of rock + Final gravitational potential energy
[tex](0.5) m v_{i}^{2} - \frac{GMm}{r_{i}} = (0.5) m v_{f}^{2} - \frac{GMm}{r_{f}} \\(0.5) v_{i}^{2} - \frac{GM}{r_{i}} = (0.5) v_{f}^{2} - \frac{GM}{r_{f}} \\(0.5) (136)^{2} - \frac{(6.67\times10^{-11}) M}{(7514000)} = (0.5) (392)^{2} - \frac{(6.67\times10^{-11}) M}{(2823000)} \\M = 4.582\times10^{21} kg[/tex]
