A solid sphere with a diameter of $\backslash (0\mathrm{.}15\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash )$ is released from rest; it then rolls without slipping down a ramp, dropping through a vertical height of $\backslash ($ h$\_\{1\}=0\mathrm{.}65\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash ).$ The ball leaves the bottom of the ramp, which is $\backslash ($ h$\_\{2\}=1\mathrm{.}15\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash )$ above the floor, moving horizontally.

$($a$)$ Through what horizontal distance $\backslash ($ d $\backslash )$ does the ball move before landing? $\backslash (\backslash$checkmark $\backslash$mathrm$\{$m$\}\backslash )$

$($b$)$ How many revolutions does the ball make during its fall? $\backslash (\backslash$times $\backslash )$ rev

$($c$)$ If the ramp were to be made frictionless, how would the distance $\backslash ($ d $\backslash )$ change? Choose one answer only,

increase

stay the same

decrease

could be any of these