Given, Height of transmitting anteena (HT)+ height of receiving anteena (HR)=160m Radius of earth, Re=6400‌km Let, range = d If height of transmitting antenna be x then, height of receiving anteena = 160 - x We know that, d=√2RhT+√2RhR=√2R[√hT+√hR] =√2×R[√x+√160−x] =√2R[√x+√160−x] For maximum range
d
dx
(d)=
d
dx
√2R[√x+√160−x]=0 ⇒
d
dx
[√x+√160−x]=0 ⇒
1
2
x−
1
2
−
1
2
(160−x)−
1
2
=0 ⇒
1
2
1
√x
=
1
2
1
√160−x
⇒x=160−x ⇒2x=160 ⇒ x = 80 ∴ Maximum range (dmax)=√2R[√x+√160−x] =√2×6400[√80+√160−80] =80√2[√