$[5$ pts$]$ Show that for vehicles with more than one articulation points, such as a tractor$-$trailer com$-$

bination, the width required to turn is

$U=u+R-\sqrt[\phantom{2}]{R^2-{\displaystyle \underset{?}{\overset{?}{}}}{L}_i^2}$

where $u$ is the width of the vehicle, $R$ is the radius of the curve, and $L_i$ is the wheelbase of vehicle

between consecutive articulation points.