$7\mathrm{.}5\mathrm{.}14.[$Level $2]$ The figures illustrate two scenarios that serve as extremely simplified models for human fall dynamics. In $($a$)$ we model the human as a rigid bar of length $\backslash ($ L $\backslash )$ and mass $\backslash ($ m $\backslash )$ that's pivoted at $\backslash ($ O $\backslash ).$ This lets us approximate the fall as a rotation about the feet. In $($b$)$ we model the falling body as a rigid bar $($mass $\backslash ($ m $\backslash )$ and length $\backslash ($ L $\backslash ))$ that's free to slide without friction along the ground. This lets us model a person slimnina mninn

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a$.$ Calculate the velocity with which the end $\backslash ($ A $\backslash )$ of the rod, the person's "head," strikes the ground for each case.

b$.$ What is the body's rotation rate just before impact?