An astronaut is approacing the moon. He sends a radio wave of frequency `5 xx 10^(9) Hz` towards the moon. The frequency of the radio echo received by him has a frequency `9 xx 10^(4) Hz` more than that of real frequency. The relative velocity of the rocket with respect to the moon is

Options

A. 1.35 km/s
B. 2.70 km/s
C. 4.05 km/s
D. 5.40 km/s

Answer

D

Explanation

`n = 5 xx 10^(9)Hz, Delta n = 9 xx 10^(4) Hz`
`c = 3 xx 10^(8) m//s, v = ?`
`(Delta n)/(n) = (v)/(c)`
`:. v = (Delta n xx c)/(n)`
`= (9 xx 10^(4) xx 3 xx 10^(8))/(5 xx 10^(9))`
`v = 5.4 xx 10^(3) m//s = 5.4 km//s`