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

Answer:

897.465 N

Step-by-step 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

$W_1=m\frac{GM}{R^2}\\\Rightarrow mGM=W_1R^2$

$W_2=m\frac{GM}{(R+h)^2}\\\Rightarrow mGM=W_2(R+h)^2$

Now

$W_1R^2=W_2(R+h)^2\\\Rightarrow W_2=\frac{W_1R^2}{(R+h)^2}\\\Rightarrow W_2=\frac{900\times (6.3781\times 10^6)^2}{(6.3781\times 10^6+9000)^2}\\\Rightarrow W_2=897.465\ N$

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