91影视

If you are at the top of a tower of height h above the surface of the earth, then it can be shown by figure.

Here, the distance from the centre of earth to top of tower is h+R.

In the triangle inscribed in the circle, it can write $\cos 胃=\frac{R}{R+h}$.

Therefore, the surface is,

$$\begin{gathered} =\sqrt{2\left(2.093脳{10}^7\right)}h \\ s=\frac{6470\sqrt{h}}{5280} \\ s=1.225\sqrt{h} \end{gathered}$$

Or, in another words

$s=\sqrt{\frac{3h}{2}}miles$

By the expansion of$\sec 胃$

$\sec 胃=1+\frac{{胃}^2}{2}+\frac{5{胃}^2}{24}+鈥�.$

According to the given statement, taking first two terms of the expansion:

$$\begin{gathered} \frac{h}{R}=1+\frac{{胃}^2}{2}-1 \\ \frac{h}{R}=\frac{{胃}^2}{2}l \\ 胃=\sqrt{\frac{2h}{R}} \end{gathered}$$

Therefore, the distance along the surface of the earth is

$$\begin{gathered} s=R胃 \\ s=R\sqrt{\frac{2h}{R}} \\ s=\sqrt{2Rh} \end{gathered}$$

Now, to show the distance in miles, it knows that radius of earth in feet is,

$\mathit{R}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{093}\mathbf{脳}{\mathbf{10}}^{\mathbf{7}}\mathbf{\text{feet}}$

Therefore, the distance in feet is

$$\begin{gathered} s=\sqrt{2\left(2.093脳{10}^7\right)}h \\ s=6470\sqrt{h} \end{gathered}$$

$$\begin{gathered} s=\sqrt{2\left(2.093脳{10}^7\right)}h \\ s=\frac{6470\sqrt{h}}{5280} \\ s=1.225\sqrt{h} \\ \text{or} \\ s=\sqrt{\frac{3h}{2}}\text{miles} \end{gathered}$$