Question

The weight w of an object above the Earth varies inversely as the square of the distance d from the centre of the earth. If an astronaut weighs 80 kg on the surface of the earth, what would this weight be at an altitude of 1000 km? Assume the radius of the Earth to be 600 km. Give your answer correct to the nearest kg.

Answer 1

11 kg

Step-by-step explanation:

Given weight in kg ∝ d² where d is the distance of the object from the center of the earth

We can write this as an equatio

w = (k/d²) where is a constant

On the surface of the earth, d = 600, w = 80 so we get

80 = k/600² ==> k = 600² ( 80) = 600 x 600 x 80 (1)

At 1000 km altitude, the actual distance of the astronaut from the center of the earth is 1000 + 600 - 1600 km

So we get another equation w' = k/1600²

were w' is the weight of the astronaut at an altitude of 1000km

Using the value of k from (1) we get

w' = (600 x 600 x 80)/(1600 x 1600) = 11.25kg = 11 correct to the nearest kg