Question

The gravitational potential energy, ‘G’ of an object is directly proportional to its height, ‘h’ above

the surface of Earth. When the object is at a height of 40 meters above Earth, its gravitational
potential energy is 2200 joules. Find
I. An equation connecting G and h.
II. The gravitational potential energy of the object when it is at a height of 22 meters above the
surface of Earth.
III. The height of the object above the surface of Earth when it has a gravitational potential
energy of 3025 joules.

Answer 1

see explanation

Explanation:

Given that G is directly proportional to h then the equation relating them is

G = kh ← k is the constant of proportion

To find k use the condition h = 40 when G = 2200, then

2200 = 40k ( divide both sides by 40 )

55 = k

1

G = 55h ← equation of proportion

11

When h = 22, then

G = 55 × 22 = 1210 joules

111

When G = 3025, then

3025 = 55h ( divide both sides by 55 )

h = 55 m