You are playing with a toy in which a marble launched by a spring rolls along a track full of loop-the-loops and curves with almost no energy dissipated. You want the marble to have a speed of \(0.70 \mathrm{~m} / \mathrm{s}\) when it arrives at the top of a loop that is \(0.30 \mathrm{~m}\) higher than the marble's position when you launch it.

(a) What initial speed must the marble have? 

\((b)\) If the marble has an inertia of \(5.0 \mathrm{~g}\) and the spring has a spring constant of \(13 \mathrm{~N} / \mathrm{m}\), how far back do you need to pull the spring on the level launching chute to get the marble to have this initial speed?