(Solved): The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in t ...

The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure below. If the spring is compressed a distance of $0.080\mathrm{m}$ and the gun fired vertically as shown, the gun can launch a 21.0-9 projectile from rest to a maximum height of $22.0\mathrm{m}$ above the starting point of the projectile. (a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height. This answer has not been graded yet. (b) Neglecting all resistive forces, determine the spring constant. $x$ Your incorrect answer may have resulted from roundoff error, Make sure you keep extra significant figures in intermediate steps of your calculation. $\mathrm{N}/\mathrm{m}$ (c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where $x=0$ ), as shown in Figure $(b)$. $x$ Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation. $\mathrm{m}/\mathrm{s}$