Q$\mathrm{.}3$ While driving through a road work$-$zone, traffic barriers narrowed the lane and were

positioned $8$ feet from the drivers. Assume that drivers keep their eyes on barrier at an angle of

$2\mathrm{.}0$ degrees, with a critical angular rate of change of $0\mathrm{.}006$ rad$/$s$.$

$($a$)$ Calculate the appropriate speed limit in mph to ensure safe navigation through the

work zone. $(10$ points$)$

$($b$)$ How far should the barrier be located from the driver's path to allow a speed limit of

$35$ mph$?(15$ points$)$