$1.$ You know your mass $($M$)$ and the mass of each of three apples you are carrying $($mo$).$ You also know your throwing speed $($vo$).$ You are standing on a frictionless surface. Compare the following cases. A$)$ You throw all three apples at the same time to your left with your throwing speed vo$,$ causing you to recoil to the right with a speed vf$.$ B$)$ You throw each apple one by one, again to the left with your throwing speed of vo$.$ Which is larger? Your final speed, vf$,$ in case A or case B$?$

$2.$ You know the moment of inertia Io and the radius R of a wheel. You connect this wheel to a frictionless bearing and then wrap a thin and low$-$mass thread around the edge of the wheel. You tie a small object whose mass you measure to be mo to the dangling end of the thread. At time$=0$ you release the small mass from rest. When t$=$t$\_$f$,$ how far has the small object fallen, H$?$