Shnol D.e.

A boy and his father are standing on the seashore. If the boy stands on tiptoe, his eyes will be at a height of 1 m above the sea surface, and if he sits on his father's shoulders, then at a height of 2 m. How many times farther will he see in the second case. (Find the answer with an accuracy of 0.1, the radius of the Earth is considered to be 6000 km.)
From a point at a height $h$ above sea level, the visible distance is $d=\sqrt{(R+h)^{2}-R^{2}}=\sqrt{2 R h+h^{2}}$, where $R$ is the radius of the Earth (see figure). If $h<<R$, then with sufficient accuracy $d=\sqrt{2 R h}$. Therefore, the desired ratio can be considered equal to $\sqrt{2}$ or 1.4.

![](https://cdn.mathpix.com/cropped/2024_05_06_76207e7feb35677daaaeg-40.jpg?height=1212&width=1089&top_left_y=0&top_left_x=490)

## Answer

1.4 times.

Send a comment