Chapter 26, Problem 65A

To determine

To Find: The speed of the moving object with respect to the radar.

Answer to Problem 65A

The velocity of the object is $26.365\text{m/s}$ .

Explanation of Solution

Given:

Frequency of transmitter $\text{=}\text{10}\text{.525}\text{GHz}$

Doppler shift frequency $\text{=}1850\text{Hz}$

Formula:

The equation of velocity in Doppler Effect

  $V_{\text{target}}=\frac{c{f}_{\text{Doppler}}}{2f_{\text{transmitted}}}$  ...... (1)

Here $f_{\text{Doppler}}$ is the Doppler shift frequency, $f_{\text{transmitted}}$ is frequency of transmitted wave, $V_{\text{target}}$ is the velocity of target and $c$ is the speed of light.

Calculation:

Substitute $1850\text{Hz}$ for $f_{\text{Doppler}}$ , $\text{10}\text{.525}\text{GHz}$ for $f_{\text{transmitted}}$ in equation (1)

  $\begin{array}{c}{V}_{\text{target}}=\frac{c{f}_{\text{Doppler}}}{2f_{\text{transmitted}}}\\ =\frac{3\times {10}^8\times 1850}{2\times 10.525\times {10}^9}\\ =26.365\text{m/s}\end{array}$

Conclusion:

Hence, the required velocity of the object is $26.365\text{m/s}$ .