==> \(\omega = \frac{{{v_{\max }}}}{a} = \frac{{10}}{4}\)

Now, \(v = \omega \sqrt {{a^2} - {y^2}} \)

==> \({v^2} = {\omega ^2}({a^2} - {y^2})\)

==> \({y^2} = {a^2} - \frac{{{v^2}}}{{{\omega ^2}}}\)

\(y = \sqrt{{a^2} - \frac{{{v^2}}}{{{\omega ^2}}}}\)

\(= \sqrt{{4^2} - \frac{5^2}{{({\frac{10}{4}})^2}}}\)

\( = 2\sqrt 3 \,cm\)