Respuesta :
Answer:
The distance above the surface of the earth is [tex]1.36\times 10^7[/tex].
Explanation:
Given that,
Acceleration due to the gravity g'= 0.995 m/s² (at height )
Acceleration due to the gravity g= 9.80 m/s² (at surface )
We know that,
The formula of gravity at height
[tex]g'=\dfrac{g}{(1+\dfrac{h}{R})^2}[/tex]
Where, h = height
r= radius of the earth
We substitute the value into the formula
[tex]0.995=\dfrac{9.8}{(1+\dfrac{h}{6.378\times10^{6}})^2}[/tex]
[tex]h=6.378\times 10^6(\sqrt{\dfrac{9.8}{0.995}}-1)[/tex]
[tex]h=1.36\times 10^7\ m[/tex]
Hence, The distance above the surface of the earth is [tex]1.36\times 10^7[/tex].
The distance above the surface of the earth will be 1.36×10⁷ m.
What is the distance?
Distance is a numerical representation of the distance between two objects or locations.
The distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.
The given data in the problem is;
g' is the acceleration due to the gravity at height = 0.995 m/s²
g is the acceleration due to the gravity at the surface = 9.80 m/s²
The formula for the gravity at height h is found as;
[tex]\rm g'=\frac{g}{(1+\frac{h}{R})^2 } \\\\\ 0.995=\frac{9.81}{(1+\frac{h}{6.378\times 10^6})^2 } \\\\ \rm h= 6.378 \times 10^6 (\sqrt{\frac{9.8}{0.995} } -1 \\\\ h= 1.36 \times 10^7 \ m[/tex]
Hence the distances above the surface of the earth will be 1.36×10⁷ m.
To learn more about the distance refer to the link;
https://brainly.com/question/26711747
