Final answer:
The monkey wrench would impact at approximately 7.5 km/s, closest to option c. For the spacecraft landing on an asteroid, the correct gravitational acceleration is about 0.195 m/s², which is not provided in the question's options.
Step-by-step explanation:
The subject of this question is Physics, specifically it relates to the concepts of gravity and falling objects. The grade level is High School.
When the monkey wrench is released at rest at the far edge of the solar system and only under Earth's gravitational influence, none of the provided speeds (9.8 m/s², 0 m/s, 7.5 km/s, 1.6 km/s) directly represent its impact velocity. Instead, they represent acceleration due to gravity, a state of no motion, typical entry speed of meteoroids, and lunar surface gravity, respectively. However, the closest physical concept related to the question would be Earth's typical orbital entry speed, which is about 7.5 km/s for objects entering from far away, so the answer is c. 7.5 km/s.
For the spacecraft landing on an asteroid, using the kinematic equations, we can calculate the approximate gravitational acceleration on the asteroid:
Initial velocity (v_i) = 5 m/s
Final velocity (v_f) = 8 m/s
Displacement (Δs) = -100 m (since it is falling towards the asteroid)
We can use the following equation to find acceleration (a):
v_f^2 = v_i^2 + 2aΔs
(8 m/s)^2 = (5 m/s)^2 + 2a(-100 m)
64 - 25 = -200a
39 = -200a
a = -39/200
Acceleration (a) = -0.195 m/s² (negative sign indicates the direction of acceleration is towards the asteroid, which is typical for gravitational acceleration)
Therefore, the approximate gravitational acceleration on this asteroid is 0.195 m/s². However, none of the options provided matches this answer, indicating a possible error in the question choices.