Modern roller coasters have vertical loops like the one shown here.

The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats.

$($a$)$ What is the speed of the roller coaster at the top of the loop $($in $\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash ))$ if the radius of curvature there is $12\mathrm{.}6$ m and the downward acceleration of the car is $1\mathrm{.}50$ g $?$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )$

$($b$)$ How high above the top of the loop $($in m $)$ must the roller coaster start from rest, assuming negligible friction?