I was messing around with a fun navigation problem the other day and thought I'd share it. I was scrolling through a weather app on my phone when I came across the sunrise and sunset times and wanted to try calculating my longitude from these times.
Most of us know that 32 degrees Fahrenheit is the temperature at which water freezes. We also know that this correlates to 0 degrees Celsius. But for many of us, our knowledge stops there and to convert between the two scales we must resort to either looking it up using some sort of app or calculating it by hand using a formula that in involves multiplying by either nine-fifths of five-ninths and adding or subtracting 32 and we often have to lookup the formula to remember which.
One of my homework problems for my modern physics course asked me to calculate the highest velocity of a particle for which the Newtonian approximation of kinetic energy is accurate to within an error of of the actual, relativistic, kinetic energy.