Question

At a particular station, the TV transmission tower has a height of $100m$. To triple its coverage range, height of the tower should be increased to

• A. 200 m
• B. 300 m
• C. 600 m
• D. 900 m

Answer 1

Answer: (D)

I et d be range
$d^2=(h+R{)}^2-R^2$
$=h^2+R^2+2RH-R^2$
$d^2=h^2+2Rh$
as $R>>>>$ h then
$d\approx \sqrt{2Rh}\dots .(1)$
Now, if coverage is to be increased 3 times $3d=\sqrt{2R{h}^{\prime }}\dots (2)$
Divide 2 and $1\frac{3d}{d}=\sqrt{\frac{2R{h}^{\prime }}{2Rh}}$
$9=\frac{h^{\prime }}{h}$
$9h=h^{\prime }$
If $h=100m$ then tower of height $900m$ is required