A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode ?

  • Option 1)

    55.4 km
     

     

  • Option 2)

     45.5 km

  • Option 3)

     54.5 km

     

  • Option 4)

    455 km

 

Answers (1)
P Plabita

As we have learnt,

 

Range of transmitting antenna -

d_{T}= \sqrt{2h_{T}R}


 

- wherein

h_{T}= height of antenna

R= Radius of earth

 

 Range = \sqrt{2Rh_r} + \sqrt{2Rh_R}

             \\= \sqrt{2\times6400\times 10^3\times 32} + \sqrt{2\times 6400\times 10^3\times 50}\\ = \sqrt{64\times 64 \times 10^5} + \sqrt{64\times 10^7}\\=6400\sqrt{10} + 8000\sqrt{10} m\\=14400\sqrt{10} = 45.5 km

 


Option 1)

55.4 km
 

 

Option 2)

 45.5 km

Option 3)

 54.5 km

 

Option 4)

455 km

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