Question

An astronaut is approaching the moon. He sends a radio wave of frequency $5\times {10}^{9}Hz$ towards the moon. The frequency of the radio echo received by him has a frequency $9\times {10}^{4}Hz$ more than that of the real frequency. The velocity of the astronaut relative to the moon is

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

Answer 1

Answer: (C)

$2.70km/s$

$v=\frac{1}{2}.\frac{\Delta v}{v}.c=\frac{1}{2}\times \frac{9\times {10}^4}{5\times {10}^9}\times 3\times {10}^8=2.7\times {10}^{3}m/s=2.7km/s$