1.

A TV transmission tower of antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level (ii) at a height of 25 m ? Calculate the percentage increase in area covered in case (ii) relative to case (i).

Answer»

2.48
`348.9%`
`150%`
`360.2%`

Solution : Here, `h_(T)=20m,R=6.4xx10^(6)m=64xx10^(5)m`
If the anteenais at ground level
Range, `d=sqrt(2h_(T)R)=sqrt(2xx20xx(64xx10^(5)))`
`=16xx10^(3)m=16km `
Areacovered, `A=PID^(2)=(22)/(7)xx(!6)^(2)=804.6km^(2)`
If the receiving ANTENNA at a height of 25m.
Range `d_(1)=sqrt(2h_(T)R)_sqrt(2h_(R)R)`
`=sqrt(2xx20xx(64xx10^(5)))+sqrt(2xx25xx64xx10^(5))`
`=16xx10^(3)+17.9xx10^(3)=33.9xx10^(3)m=33. 9km`
Area covered `A_(1)=pid_(1)^(2)=(22)/(7)xx(33.9)^(2)=3611.8km^(2)`.
PERCENTAGE increase in area `=(A_(1)-A)/(A)xx100`
`=((3611.8-804.6)/(804.6))xx100=348. 9%`


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