Respuesta :
The horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).
What is Pythagoras Theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The complete question is:
" For a typical human height of 2 meters, what is the horizon distance on A) Earth (R=6378 km); B) Mars ( 3,374 km); C) The Moon ( 1,738 km); Mars' moon Diemos ( 6 km) "
Radius touching the line which passes touching the circle (tangent) is perpendicular(to 90°) to it.
Consider the diagram attached below:
The distance D is the distance of horizon from the eyesight of viewer.
The value of h is the height of the observer.
For the triangle ABC, the length of the hypotenuse is: h + R
Other two sides which are mutually perpendicular are of length R and D.
Thus, by using Pythagoras theorem, we get:
[tex]R^2 + D^2 = (h+R)^2\\D = \sqrt{h^2 + R^2 + 2hR -R^2}\\\\D = \sqrt{h^2 + 2hR}\\[/tex]
(positive root as D is representing length, a non-negative quantity).
We're given h = 2, so we get:
[tex]D = \sqrt{4+4R} = 2\sqrt{1+R} \: \rm m[/tex]
- A) Earth (R=6378 km);
6378 km = 6378000 m
[tex]D = 2\sqrt{6379001} \approx 5051 \: \rm m \approx 5 \: km[/tex]
- B) Mars ( 3,374 km);
3374 km = 3374000 m
[tex]D = 2\sqrt{3374001} \approx 3674 \: \rm m \approx 3.7 \: km[/tex]
C) The Moon ( 1,738 km);
1738 km = 1738000 m
[tex]D = 2\sqrt{1738001} \approx 2637 \: \rm m \approx 2.6 \: km[/tex]
D)Mars' moon Diemos ( 6 km)
6 km = 6000 m
[tex]D = 2\sqrt{6001} = 154.93 \: \rm m \approx 0.15 \: km[/tex]
Thus, the horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
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