Question $3$

A falling gradient $4\%$ meets a rising gradient of $5\%$ at chainage $2450m$ and level $215\mathrm{.}50m$

At chainage $2350m,$ the underside of the bridge has a level of $235\mathrm{.}54m($as shown in

Figure $1$ with I as the centre of the parabolic curve$).$

Figure $1$

The two grades are joined by a vertical parabolic curve giving $14m$ clearance under the bridge.

$($i$)$ Determine the offset at chainage $2350m.$

$($ii$)$ What is the length of the vertical curve?

$($iii$)$ Calculate the offsets at chainage $0,50,100,150($m$)$ up to end of the curve.

$($iv$)$ Calculate the tangent levels.

$($v$)$ Based on $($iii$)$ and $($iv$),$ list the corresponding levels along the curve at the specified chainage.

$($vi$)$ Verify the answers obtained in $($v$)$ by direct substitution into the equation for the curve

$[30$ marks$]$