You lean out of your dorm window, which is \(12 \mathrm{~m}\) above the ground, and toss a \(0.12 \mathrm{~kg}\) ball up to a friend at a window \(11 \mathrm{~m}\) above you.

(a) What is the slowest initial speed at which you can throw the ball so that he just catches it?

(b) If you throw the ball at this speed and your friend misses it, what is its kinetic energy the instant before it hits the ground?

(c) Suppose you throw the ball directly downward at the speed calculated in part \(a\). What is its kinetic energy just before it hits the ground?