A 1-(GHz) Doppler radar on the ground is used to determine the location and speed of an approaching airplane. Assuming that the signal reflected from the airplane at an elevation angle of { 15.5 }^{ o } showed a time delay of 0.3 (ms) and a frequency shift of 2.64 (kHz), find the distance, height, and speed of the airplane
Question : A 1-(GHz) Doppler radar on the ground is used to determine t...
\Delta t=\frac { 2R }{ c } =0.3\times { 10 }^{ -3 }\left( s \right)
R=\frac { \Delta t }{ 2 } c=\frac { 0.3\times { 10 }^{ -3 } }{ 2 } \times 3\times { 10 }^{ 8 }
\quad =45\times { 10 }^{ 3 }\left( m \right)
or 4.5 (km)
h=R\sin { \theta } =45\times { 10 }^{ 3 }\sin { { 15.5 }^{ o } } =12\times { 10 }^{ 3 }\left( m \right) ,\quad or 12\left( km \right)
\Delta f=2f\left( \frac { u }{ c } \right) \cos { { 15.5 }^{ o } }
\rightarrow u=\frac { c\Delta f }{ 2f\cos { { 15.5 }^{ o } } } =410.8\left( m/s \right) or about 1.2 mach
