Question

Объясните, прошу! :) Готовлюсь к ЕГЭ по математике... ((( Если наблюдатель находится на небольшой высоте h над поверхностью Земли, то расстояние от него до линии горизонта можно найти по формуле l = √2Rh , где R = 6400 км – радиус Земли. Найдите наименьшую высоту, с которой должен смотреть наблюдатель, чтобы он видел линию горизонта на расстоянии не менее 6,4 км? (Ответ выразите в метрах.)

Answer 1

√(2Rh) = l
√(2 × 6400 × h) ≤ 6,4
(√(12800 × h))² ≤ (6,4)²
12800h ≤ 40,96
h ≤ 40,96 ÷ 12800
h ≤ 4096 ÷ 1280000
h ≤ 0,0032 => h(min) = 0,0032 км = 3,2 м
Ответ: 3,2 м

Answer 2

Problem Analysis

The problem asks us to find the minimum height from which an observer must be positioned in order to see the horizon at a distance of at least 6.4 km. We are given the formula l = √(2Rh), where R is the radius of the Earth (6400 km). We need to express the answer in meters.

Solution

To find the minimum height from which the observer must be positioned, we can rearrange the formula l = √(2Rh) to solve for h.

Let's solve the equation step by step:

1. Start with the equation l = √(2Rh). 2. Square both sides of the equation to eliminate the square root: l^2 = 2Rh. 3. Divide both sides of the equation by 2R: l^2 / (2R) = h. 4. Substitute the given values: l^2 / (2 * 6400) = h. 5. Simplify the equation: l^2 / 12800 = h. 6. Convert the distance l from kilometers to meters: 6.4 km = 6400 m. 7. Substitute the value of l: (6400^2) / 12800 = h. 8. Simplify the equation: 3200 = h.

Therefore, the minimum height from which the observer must be positioned to see the horizon at a distance of at least 6.4 km is 3200 meters.

Answer

The minimum height from which the observer must be positioned to see the horizon at a distance of at least 6.4 km is 3200 meters.