A mother penguin and her chick are on a flat, icy surface. The mother is lying at rest \(0.50 \mathrm{~m}\) from the edge of the water. The chick, which has one-fourth of its mother's inertia, is sliding, collides with her inelastically, and bounces back at one-eighth of its original speed. The mother wakes up as she hits the water \(0.40 \mathrm{~s}\) later.

(a) How fast was the chick going when it hit her?

(b) To a penguin paddling directly toward them at \(1.0 \mathrm{~m} / \mathrm{s}\), what is the mother's momentum before and after the collision in terms of \(m_{\text {mother }}\) ?