A solid sphere and a solid cylinder of the same radius and mass are released on a $20\mathrm{.}0$ inclined plane from the same height and at the same time. $($a$)$ Use conservation of energy to find equations for the speeds $$ and $$ at the bottom of the ramp as a function of starting height h$.($b$)$ Calculate a numerical result for the final velocities if $=50\mathrm{.}0$ cm$.($c$)$ Calculate the final angular velocities if the radius of each object is $1\mathrm{.}00$ cm$.($d$)$ Calculate the time it takes for each object to get to the bottom of the ramp.