Direct and inverse proportions

Question

The weight of an object is inversely proportional to the square of the distance from the object to the centre of the earth. An astronaut weighs 800 newtons (N) at sea level (6500 km from the centre of the earth).

a. Find the weight of the astronaut when he is orbiting 2.5 x 10⁴ km above sea level.

b. Calculate how far above the centre of the earth the astronaut is when his weight is half of that at sea level

Answer 1

w = k/d^2

800 = k6500^2= 42,250,000k

k = 42250000/800= 422,500/8 = 52,812.5

w = 52,812.5/d^2 = 52812.5/(2.5 x 10^4) = 52,812.5/25,000

w = 2.1125 Newtons when 2.5 x 10^4 km high

half of 800 n = 400 n

400 = 52,821.25/d^2

d^2 = 52,821.25/400 =132.03125

d = sqr(132.03125)

= about 11.49 km

Bao, as in Bao Dai? last Emperor of Vietnam?