$1-21($a$)$ What fractional error does one make in using $\frac{1}{2}M{v}^2$ for the kinetic energy of a body if its speed is

$(1)3\frac{m}{sec}$

$(2)300\frac{m}{sec}($the speed of sound in air$)$

$(3){10}^4\frac{m}{sec}($the speed a body needs to escape from the earth$)$

$(4)0\mathrm{.}1$ c

$(5)0\mathrm{.}9c$

$($b$)$ If the experimental error in a measurement of $v$ is $1\%($approximately$),$ how large must $v$ be before relativistic corrections become significant?