Final answer:
Using Hubble's Law and the value of the speed of light, galaxies moving away from us at 2.0% of the speed of light are estimated to be approximately 2.8×10⁹ light-years away from us, which rounds to 2×10⁹ light-years, option (c).
Step-by-step explanation:
To estimate the average distance of galaxies moving away from us at 2.0% of the speed of light, we can use the Hubble's Law, which relates the velocity of a galaxy moving away from us due to the expansion of the universe to its distance.
The formula is V = H₀ × d, where V is the velocity, H₀ (the Hubble constant) is typically about 70 kilometers per second per megaparsec (km/s/Mpc), although it can vary slightly based on different observations, and d is the distance in megaparsecs. Given that 2.0% of the speed of light (which is approximately 299,792 km/s) equals about 6,000 km/s, we can calculate the distance by rearranging Hubble's Law as d = V/H₀.
Using the Hubble constant as 70 km/s/Mpc, the calculation becomes d = 6000 km/s / 70 km/s/Mpc, which gives us d ≈ 85.7 Mpc. To convert megaparsecs to light-years, we use the conversion factor 1 Mpc ≈ 3.26 million light-years, yielding d ≈ 85.7 Mpc × 3.26 million light-years/Mpc ≈ 279 million light-years, which we can approximate as 2.8 × 10⁹ ly. Therefore, the answer closest to this calculation is (c) 2×10⁹ly.