(Solved): A 1.50kg solid, uniform sphere of radius 0.120m is released from rest at point A in the figure ...

A $1.50\mathrm{kg}$ solid, uniform sphere of radius $0.120\mathrm{m}$ is released from rest at point A in the figure below, its center of gravity a distance of $1.80\mathrm{m}$ above the ground. The sphere rolls without slipping to the bottom of an incline and back up to point $B$ where it is launched vertically into the air. The sphere then rises to its maximum height $h$ rax at point $C$. (a) At point B, find the sphere's transiational speed $v_B$ (in $\mathrm{m}/\mathrm{s}$ ). $\mathrm{m}/\mathrm{s}$ (b) At point $B$, find the sphere's rotational speed ${?}_B$ (in rad/s). $\times \mathrm{rad}/\mathrm{s}$ (c) At point C, find the sphere's rotational speed ${?}_{\mathrm{C}}$ (in rad/s). $\mathrm{rad}/\mathrm{s}$ (d) At point $c$, find the maximum height $h_{\max }$ of the sphere's center of gravity (in $m$ ).