You are on an airplane traveling with a constant velocity at an altitude of 20,000m. What is the acceleration of gravity at that altitude? The earth's radius is 6.37 x 10^6m.

A) 9.81 m/s^2
B) 9.78 m/s^2
C) 9.75 m/s^2
D) 9.72 m/s^2
E) 9.69 m/s^2

Question

You are on an airplane traveling with a constant velocity at an altitude of 20,000m. What is the acceleration of gravity at that altitude? The earth's radius is 6.37 x 10^6m.

A) 9.81 m/s^2
B) 9.78 m/s^2
C) 9.75 m/s^2
D) 9.72 m/s^2
E) 9.69 m/s^2

fifciol · Answer

Gravitational force:
$$F=\frac{GMm }{ r^2 }$$ 
where r is the distance from the surface of the Earth
according to Newton's second law :
$$F=ma$$
so
$$ma=\frac{GMm }{ r^2 }\rightarrow a=\frac{GM }{ r^2 }$$ 
our problem looks like this:
|dw:1376074097528:dw|
where a=20 000m
so the acceleration is simply:
 $$a=\frac{GM }{ (R+a)^2 }$$