Question

1.17 A man weighs 900N on the surface of the earth. Compute his weight in an airplane flying at an elevation of 9000 m

Answer 1

897.465 N

Explanation:

Weight of man on the surface = 900 N = W₁

Weight of man at 9000 m = W₂

Mass of man = m

G = Gravitational constant

h = height of man = 9000 m

M = Mass of Earth

R = Radius of Earth

`W_1=m(GM)/(R^2)\\\Rightarrow mGM=W_1R^2`

`W_2=m(GM)/((R+h)^2)\\\Rightarrow mGM=W_2(R+h)^2`

Now

`W_1R^2=W_2(R+h)^2\\\Rightarrow W_2=(W_1R^2)/((R+h)^2)\\\Rightarrow W_2=(900* (6.3781* 10^6)^2)/((6.3781* 10^6+9000)^2)\\\Rightarrow W_2=897.465\ N`

∴ His weight in an airplane flying at an elevation of 9000 m is 897.465 N