(Solved): An airplane is flying straight and level at a constant speed v0 when it starts climbing along a ...

An airplane is flying straight and level at a constant speed $$v_0$$ when it starts climbing along a path described by the equation $$y=h+$$ $$?x^3$$, where $$h$$ and $$?$$ are constants. Let $$g$$ denote the acceleration due to gravity. If $$?=0.05\times 10^{?3}{\mathrm{m}}^{?2}$$ and $$v_0$$ remains constant, find $$v_0$$ such that the magnitude of the acceleration of the airplane is equal to $$3\mathrm{g}$$ for $$x=345\mathrm{m}$$. (Round the final answer to four decimal places.) The speed of the airplane is $$\mathrm{m}/\mathrm{s}$$.