$(20$pts$)$ An elevated expressway goes through an urban area and crosses a local street as

shown in the figure below. The partial cloverleaf exit ramp is on a $3$ percent downgrade and

all vehicles leaving the motorway should stop at the intersection with the local street before

merging. Determine the length required for the ramp for the following conditions:

Maximum speed on the motorway $=55mph$

Distance between exit sign and exit ramp $=260ft$

Letter height of road sign $=3$ inches

Expressway grade $=-2\%$

Assume that a driver can read a sign within a cone of vision at a distance of $60$ ft for each

inch of letter height, and the driver sees the stop sign immediately on entering the ramp.