Answer:
For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.
Explanation:
The force of gravity comes from Newton's second law with the force the universal attraction
F = ma
F =
we substitute
= m₁ a
where Re is the radius of the Earth 6.37 106 m
a =
In general, the height is much less than the radius of the earth, therefore the term ha / Re is very small and we can use a series expansion leaving only the first fears.
(1 + x)⁻² = 1 -2x + x²
we substitute
a = g₀ ( )
with
g₀ =
let's launch the expression.
* For small height compared to the radius of the earth we can neglect the last term
g = g₀
* For height comparable to the radius of the Earth
g = g₀
We see that the acceleration of gravity is decreasing.
For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.
