Question

# The frequency of a radar is 780MHz.  The frequency of reflected wave from an airoplane is increased by 2.6kHz.  The velocity of the airoplane is

A
2km/s
B
1km/s
C
0.5km/s
D
0.25km/s

Solution

## The correct option is B 0.5km/sGiven : $$\delta=780\ MH{z}=780\times 10^{6}\ H{z}$$$$\delta^{'}=2.6\times 780\times 10^{6}\ H{z}$$$$v_{s}=0\ m/s$$$$v=330 m/s$$By Doppler effect formula$$\delta^{'}=\delta\left ( \dfrac{v-v_{0}}{v-v_{3}} \right )$$$$2.6\times 780\times 10^{6}=780\times 10^{6}\left ( \dfrac{330+v_{p}}{330-0} \right )$$$$2.6\times 330=330+v_{p}$$$$\Rightarrow v_{p}=330(1.6)$$$$=500\ m/s$$$$=0.5\ km/s$$Physics

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