Question

Расстояние от наблюдателя,находящегося на высоте h м над землей,до наблюдаемой им линии горизонта вычисляется по формуле l=общий корень Rh/500,где R=6400 км-радиус Земли.Человек,стоящий на пляже,видит горизонт на расстоянии 8 км.На сколько метров нужно подняться человеку,чтобы расстояние до горизонта увеличивалось до 12,8 км?

Answer 1

Корень из (6400h/500)=4

 корень из (64h/5)=4

64h/5=16

h=5/4

h=1.25 м

Ответ: 1,25.

 

Answer 2

Calculation of Distance to the Horizon

The formula to calculate the distance from an observer, standing at a height of h meters above the ground, to the observed horizon line is given by:

l = √(Rh/500)

Where: - l is the distance to the horizon in kilometers - R is the radius of the Earth, which is 6400 km - h is the height of the observer above the ground in meters

To find out how many meters a person needs to raise themselves in order to increase the distance to the horizon to 12.8 km from the initial distance of 8 km, we can set up the following equation:

√(6400h/500) = 12.8 - 8

Simplifying the equation:

√(6400h/500) = 4.8

Squaring both sides of the equation:

6400h/500 = 4.8^2

Simplifying further:

6400h/500 = 23.04

Cross-multiplying:

6400h = 500 * 23.04

Solving for h:

h = (500 * 23.04) / 6400

Calculating the value:

h ≈ 1.8 meters

Therefore, the person needs to raise themselves by approximately 1.8 meters in order to increase the distance to the horizon from 8 km to 12.8 km.

Please note that the above calculation assumes a perfectly spherical Earth and does not take into account atmospheric refraction or other factors that may affect the visibility of the horizon.