Question

A rocket of mass 550000 kg is delivering cargo to the ISS. While it is docked it had a GPE of 2.2x10*12 J. Calculate the height of the ISS

Answer 1

The height of the ISS based on the provided gravitational potential energy and mass of the docked rocket is approximately 408 kilometers above Earth's surface.

Step-by-step explanation:

To calculate the height of the International Space Station (ISS) given the gravitational potential energy (GPE) of a docked rocket, we can use the formula GPE = m * g * h, where m is the mass of the rocket, g is the acceleration due to Earth's gravity, and h is the height above Earth's surface. The student provided that the GPE is 2.2 x 1012 J, and the mass of the rocket is 550,000 kg.

First, we assume that the acceleration due to gravity (g) near the surface of the Earth is approximately 9.81 m/s2. We can rearrange the formula to solve for height (h):

h = GPE / (m * g)

This gives us:

h = (2.2 x 1012 J) / (550,000 kg * 9.81 m/s2)

Now, we calculate the height:

h = 2.2 x 1012 / (550,000 * 9.81)

h = 4.08 x 105 meters or 408 kilometers.

Therefore, the ISS is approximately 408 kilometers above Earth's surface when the rocket is docked with that given GPE.