Question $(1)$:

A car was moving by its own weight $($without applying any tractive effort or brakes$)$ on a $1\mathrm{.}0\backslash \%$ downgrade paved surface at a constant speed $\backslash (32\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ).$ The mass of the car is $1900$ kg with frontal area $\backslash (5\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ Assuming that gravity is $\backslash (9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash )$ and the density of the air is $\backslash (1\mathrm{.}0588\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ you are required to calculate the drag coefficient of that car.

Question $(2)$:

A front$-$wheel drive car has mass of $1950$ kg $,$ wheel base $3\mathrm{.}95$ m $,$ and center of gravity at height $440$ mm above roadway surface. You are required to calculate the distance between the center of gravity and the front axle of that car to ensure that it will not slide when a braking force of $12\mathrm{.}230$ kN is applied at speed $\backslash (120\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ given that the coefficient of road adhesion is $0\mathrm{.}80$ and assuming that gravity is $\backslash (9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash ).$

Question $(3)$:

A driver was driving his car on a $3\mathrm{.}5\backslash \%$ downgrade road when he collided with a large object that was thrown on the road surface from a nearby building. The tire marks indicate that the driver has applied the brakes at distance $180$ m from the point of the collision. The damage analysis indicates that the driver has applied a deceleration rate of $\backslash (3\mathrm{.}6\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash )$ and he has collided with the object at a speed of $\backslash (36\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ).$ You are required to calculate the speed of the car at the time when the driver applied the brakes $($in km$/$h$).$

Question $(4)$:

An equal$-$tangent vertical curve has an initial grade $\backslash (-3\mathrm{.}5\backslash \%\backslash )$ and final grade $\backslash (+1\mathrm{.}5\backslash \%\backslash )$ with its PVI located at station $\backslash ((2+415)\backslash )$ and elevation $20\mathrm{.}65$ m $.$ The stations $\backslash ((2+455)\backslash )$ and $\backslash ((2+495)\backslash )$ on that curve should be at the same elevation. You are required to calculate the following:

a$)$ The required length of that curve to meet the above design requirements.

b$)$ The station and elevation of the lowest point on that curve.

Question $(5)$:

A horizontal curve has a design speed of $\backslash (80\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ with four lanes in each direction $($lane width $3\mathrm{.}60$ m $)$ and $4\mathrm{.}5$ m median. The design radius, $\backslash ($ R $\backslash ),$ of that curve is $350$ m $,$ and the superelevation rate is $\backslash (6\backslash \%\backslash ).$ The curve's point of curvature is located at station $\backslash ((4+231\mathrm{.}54)\backslash )$ and point of intersection is located at station $(\backslash (4+325\mathrm{.}32\backslash )).$ Assuming that the gravity is $\backslash (9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash ),$ you are required to calculate the following:

a$.$ The coefficient of side friction on that curve.

b$.$ The station of $\backslash ($ P T $\backslash )$ on that curve.

Question $(6)$:

A horizontal curve has its middle ordinate, $\backslash ($ M$,150\mathrm{.}00\backslash$mathrm$\{$~m$\}\backslash )$ and its external distance, $\backslash ($ E$,300\mathrm{.}00\backslash$mathrm$\{$~m$\}\backslash ).$ That curve has three lanes in each direction with each lane is having a width of $3\mathrm{.}50$ m $.$ There is also a median with a width of $8\mathrm{.}60$ m $.$ You are required to calculate the following:

a$.$ The central angle of that curve.

b$.$ The available stopping sight distance if a fence is located at distance $8\mathrm{.}85$ m from the inside edge of the inner lane on that curve.