Question

In​ physics, it is established that the acceleration due to​ gravity, g (in meters divided by sec squared) in meters/sec²​, at a height h meters above sea level is given by the formula below. ​
`g(h) = (3.99 x 10^(14))/((6.374 x 10^6 + h)^2)` where 6.374 x 10⁶⁶ is the radius of Earth in meters.

A certain building is 458 meters tall. What is the acceleration due to gravity at the top at the top of the building​? ​g(h) = _______ m/sec².

Answer 1

`g(h)=9.81943\ m/s^2`

Step-by-step explanation:

The given function is

`g(h)=(3.99* 10^(14))/((6.374* 10^6+h)^2)`

Now h = the height from the surface of the Earth

Here the building is 458 m tall

`g(458)=(3.99* 10^(14))/((6.374* 10^6+458)^2)`

`\Rightarrow g(458)=9.81943\ m/s^2`

So,

`g(h)=9.81943\ m/s^2`