A 0.59g mass of Glynnium goes through a nuclear fission reaction. The energy from the process is used to lift a 97211kg Saturn 5 rocket into orbit. If the mass is transformed with 1% efficiency, what height does the rocket reach?

Express your answer in kilometers

To determine the height the rocket reaches, we need to calculate the energy produced by the nuclear fission reaction and then use that energy to calculate the potential energy gained by lifting the rocket.

Step 1: Calculate the energy produced by the nuclear fission reaction.
Given that the mass of Glynnium transformed is 0.59g and the transformation efficiency is 1%, we can calculate the energy produced using Einstein's famous equation, E=mc^2.
First, convert the mass to kilograms: 0.59g = 0.59/1000 = 0.00059kg.
Next, calculate the energy produced: E = (0.00059kg) × (3 x 10^8 m/s)^2.

Step 2: Calculate the potential energy gained by lifting the rocket.
Given that the rocket's mass is 97211kg, the potential energy gained can be calculated using the equation: PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and h is the height.
We need to find h.

PE (Potential Energy) = E (Energy produced)

Rearranging the equation, we get:
h = PE / (mg)

Substituting the values:
h = E / (97211kg * 9.8 m/s^2)

Step 3: Convert the height to kilometers.
Once we have the height in meters, we can convert it to kilometers by dividing by 1000.

Let's calculate the answer:

Step 1: Calculate the energy produced by the nuclear fission reaction:
E = (0.00059kg) × (3 x 10^8 m/s)^2

Step 2: Calculate the potential energy gained by lifting the rocket:
h = E / (97211kg * 9.8 m/s^2)

Step 3: Convert the height to kilometers:
Height (in kilometers) = h / 1000.

By following these steps and performing the necessary calculations, you can determine the height the rocket reaches.