A tree is located $35\mathrm{.}5$m from the edge of road A and $37\mathrm{.}5$ m from the edge of the road B$,$ which are crossing at an uncontrolled intersection. If the maximum speed on road B is $70$kmph$,$ what should the speed limit on road A be such that the minimum sight distance is provided to allow the drivers of approaching vehicles to avoid collision by adjusting their speeds? Use perception reaction time as $2$s and an additional $2$s for the driver to actuate braking. Take the coefficient of friction as $0\mathrm{.}38.$ Assume the width of a lane is $3\mathrm{.}5$m$.$