Program $2$ Basic: Light Travel

Goal:

If you have taken some physics courses, you may remember that time passes more slowly for astronauts

on a spaceship traveling at speeds approaching the speed of light than for people on earth. Moreover,

the mass of the spaceship increases as it approaches the speed of light $-$ which is an estimate of how

much more energy must be expended as the spaceship approaches the speed of light.

In this program, you will ask the user how fast they plan to travel then tell them how long it will take to

get to various star systems and what the new mass of the spaceship will be$.$

You will use Einstein's equation to do this.

Einstein's Factor Equation:

Einstein defined a simple equation that provides a factor that indicates the change in time and mass

based upon velocity:

$f=\frac{1}{\sqrt[\phantom{2}]{1-\frac{v^2}{c^2}}}$

In this formula, $v$ represents velocity and $c$ the speed of light.

But what is a factor? Well, it's the same thing you used in the last program $-$ some number we multiply

or divide by to do a conversion. In this case, the factor, $f,$ represents how much the travel time is

reduced and the spaceship's mass is increased $-$ which means we need to multiply to get the new mass

of the spaceship and divide to determine how long it will take to get to a star system.

Specifications:

Prompt the user for input "Velocity as a $\%$ of the speed of light: $"$ and accept the input as a

float.

NOTE: Your program will need to do some middle school math with the input. Basically,