A clever engineer designs a "sprong" that obeys the force law $F_x=-q(x-x_e{)}^3,$ where $x_e$ is the equilibrium position of the end of the sprong and $q$ is the sprong constant. For simplicity, we'll let $x_e=0m.$ Then $F_x=-q{x}^3.$

Part C

A sprong$-$loaded toy gun shoots a $21$ g plastic ball. What is the launch speed if the sprong constant is $4\mathrm{.}2{10}^4\frac{N}{m^3}$ and the sprong is compressed $13$ cm $?$ Assume the barrel is frictionless.

Express your answer with the appropriate units.

$v=$