A \(0.075-\mathrm{kg}\) disk initially at rest in the Earth reference frame is free to move parallel to a horizontal bar through a hole at the disk's center. The disk is struck face-on by a \(0.050-\mathrm{kg}\) paintball traveling at \(11 \mathrm{~m} / \mathrm{s}\), as illustrated in Figure P6.51.

(a) What is the initial relative velocity of the disk and the paintball?

(b) What is their reduced inertia?

(c) If all the paint stays on the disk, what percentage of the original kinetic energy is converted to internal energy?

(d) What is the change in kinetic energy measured by someone riding a bicycle at the velocity of the paintball before the collision?

(e) Confirm your answer to part \(d\) by calculating the final and initial kinetic energies in the cyclist's reference frame. 

Data from Figure P6.51