Question

A TV tower has a height of 60 m. What is the maximum distance and area up to which TV transmission can be received? (Take radius of earth as 6.4 xx 10^6 m).

Answer 1

•A TOWER HAS A HEIGHT OF 60m, THE MAXIMUM DISTANCE would be 27.7 kms and the AREA would be 2,411 km².

• The MAXIMUM DISTANCE of a transmitting tower can be found using

dmax = ✓2Rh

=✓2x6.4x10^6x60

=27.7 kms

• The mathematical expression for area is AREA = 2πrh

=2xπx27.7x60

=2411 km²

Answer 2

Given :

Height of TV tower :

h = 60 m

Radius of earth :

R = $6.4\times 10^{6} m$

To Find :

Maximum distance and area up to which TV transmission can be received =?

Solution :

∴The formula used distance up to which transmission can be received is :

$d=\sqrt{2rh}$    -(1)

where d , r and h are :

transmission distance , radius of earth and height of tower respectively.

And the formula for Area up to which transmission can be received is :

$A= \pi d^{2}$  -(2)

Now putting the given values in (1) we get d as ;

$d=\sqrt{2\times 6.4\times 10^{6}\times 60 } m \\d=8.76\times 10^{3} m$

$A= \pi (8.76\times 10^{3}) ^{2} \\A=3.14\times 76.8\times 10^{6}\\ A= 241.152\times 10^{6} m^{2}$Now putting value of d in equation (2) we get A as :

So the maximum distance up to which TV transmission can be received is 8760 m and maximum area up to which transmission can be received is 241152000 square meter .