Question $2(15$ points$)$:

The speed limit on a highway is $60mph,$ and a particular segment of this highway has a $3\%$

downgrade. Ahead, there is a temporary work zone where the speed limit is reduced to $30mph.$

To inform drivers of this reduced speed, a work zone speed limit sign will be installed. The

letters on the sign are $10$ inches high, and it is assumed that a driver can read a road sign from a

distance of $30$ feet for each inch of letter height. Also, consider that the driver's perception$-$

reaction time is $2\mathrm{.}5$ seconds.

a$)(5$ points$)$ Calculate the distance a driver will travel from the moment they see the work

zone speed limit sign until they reduce their speed to $30mph.$

b$)(5$ points$)$ Calculate the distance at which a driver can first see the sign, based on the

assumption that a driver can read a road sign from a distance of $30$ feet for each inch of

letter height.

c$)(5$ points$)$ Determine the minimum distance at which the work zone speed limit sign

should be placed from the start of the work zone.