Question

If a galaxy is receding with a velocity of 1,400 kilometers per second, and the Hubble constant is H0 = 70 km s−1 Mpc−1. How far away is it in Mpc?

a. 10 times MpC
b. 20 Mpc
c. 0.05 Mpc
d. 0.1 Mpc
cannot say from the information given

Answer 1

The galaxy that is receding at a velocity of 1,400 kilometers per second is 20 Mpc away, using the given Hubble constant of 70 km s^{-1} Mpc^{-1}.

Step-by-step explanation:

The question asks how far away a galaxy is if it is receding with a velocity of 1,400 kilometers per second, given that the Hubble constant (H0) is 70 km s-1 Mpc-1. According to Hubble's law, the velocity (v) with which a galaxy recedes is directly proportional to its distance (d) from us, which can be written as v = H0d. To find the distance in megaparsecs (Mpc), we rearrange this equation to d = v / H0.

Given the values v = 1,400 km s-1 and H0 = 70 km s-1 Mpc-1, we can calculate the distance:

d = 1,400 km s-1 / 70 km s-1 Mpc-1

d = 20 Mpc

Therefore, the correct answer is that the galaxy is 20 Mpc away from us.