Question

A particle is moving at 0.75c relative to a lab on Earth. By what percentage is the Newtonian expression for its momentum
in error, i.e., how wrong is the classical formula? (The percentage error is the difference between the erroneous and correct
values, divided by the correct one).

Answer 1

p Newton = m v
p relativistic = m v /sqrt(1 = .75^2)
so
100(p relativistic - p newton)/p rel

here 1/sqrt(1-.75^2) = 1.512

so
100 ( 1.512 - 1)/1.512 = 33.9 %