Final answer:
The contracted length observed when a 1,000.0 m space rock is moving at 0.6 c toward an observer is approximately 800.0 m.
Step-by-step explanation:
The contracted length observed when a 1,000.0 m space rock is moving at 0.6 c toward an observer can be calculated using the concept of length contraction. According to the theory of relativity, when an object moves at relativistic speeds, its length appears shorter in the direction of motion to an observer. The formula for length contraction is given by:
L' = L / γ
Where L' is the contracted length observed, L is the proper length of the object, and γ (gamma) is the Lorentz factor given by γ = 1 / sqrt(1 - v^2/c^2), where v is the velocity of the object and c is the speed of light.
Substituting the values into the formula, we have:
L' = 1000.0 m / γ
Given that the velocity of the space rock is 0.6 c, substituting this value into the formula, we have:
L' = 1000.0 m / (1 / sqrt(1 - 0.6^2))
Simplifying the equation, we get:
L' ≈ 800.0 m
Therefore, the contracted length observed when the space rock is moving toward an observer is approximately 800.0 m. Hence, the correct option is (C) 800.0 m.