$12\mathrm{.}3.$ A $200-$lb history buff climbs up a $100-1$b$,10\mathrm{.}0-$ft ladder to recreate the Lindbergh kidnapping for curious onlookers. The ladder makes a $53\mathrm{.}13\backslash$deg angle with the ground on which there is a coefficient of static friction of $0\mathrm{.}500,$ while the other end rests on a smooth wall. $($a$)$ Find the frictional force when he has climbed up a distance $2$ feet $($measured along the ladder$).($b$)$ Find the maximum distance he can go up the ladder before his demonstration ends abruptly.