The frequency of a radar is 780 MHz. After getting reflected from an approaching aeroplane, the apparent frequency is more than the actual frequency by 2.6 kHz. The aeroplane has a speed of

Options

A. `0.25 km//sec`
B. `0.5 km//sec`
C. `1 km//sec`
D. `2 km//sec`

Answer

B

Explanation

`n' = n'' = Deltan = (2v_(s))/(v)xxn`
`Deltan = 2.6 kHz = 2.6 xx 10^(3) Hz`
and `n = 780MHz = 780 xx 10^(6) Hz`
`:. 2.6 xx 10^(3) = (2v_(s))/(3 xx 10^(8))xx780xx10^(6)`
or `v_(s) = ((2.6 xx 10^(3))(3 xx 10^(3)))/(2xx(780 xx 10^(6))) = 500 m//s`
`= 0.5 km//sec`.