Question

At certain distance from a transmitting tower, a receiver tower of height $20m$ is used to receive direct signal. Another tower is installed beyond the first, along the same line of sight to receive the signals from the same transmitter. Its height is $44$% more than the first receiving tower. Then, the separation between the two receiving towers is (Radius of Earth = $6400km$)

• A. $6.4km$
• B. $3.2km$
• C. $1.6km$
• D. $0.8km$

Answer 1

The correct option is B $3.2km$

$D_m=\sqrt{2R{h}_t}+\sqrt{2R{h}_r}$
$(D_m{)}_2-{\left(D_m\right)}_1=\sqrt{2R{h}_r}(\sqrt{1.44}-\sqrt{1})=\sqrt{40\times 64\times {10}^5}\left(0.2\right)=3.2km$.