A \(52-\mathrm{kg}\) ice skater (this value includes her body, her clothing, and several \(1.0-\mathrm{kg}\) snowballs she is carrying) is at rest on the ice. She throws a snowball to the right at \(10 \mathrm{~m} / \mathrm{s}\).

(a) What is her speed after the throw? Is her velocity to the left or to the right?

(b) Calculate the coefficient of restitution for this event. She next throws a second snowball but this time at a speed of \(20 \mathrm{~m} / \mathrm{s}\) to the left.

(c) What is her speed after this throw? Is her velocity to the left or to the right?

(d) Calculate the coefficient of restitution for this event.

(e) Calculate the change in kinetic energy in this second event. Where does the added kinetic energy come from? \((f)\) If one food calorie equals \(4184 \mathrm{~J}\), how many food calories does the skater burn when she throws the second snowball?