A car, with mass $1\mathrm{.}30$e$+03$ kg$,$ drives over a hill. The rounded crest of the hill has a radius of curvature in the vertical plane of

r $=53\mathrm{.}0$

m$.$

$($a$)$ If the car, when it reaches the top of the hill, is moving at a constant speed of $60\mathrm{.}0$ km$/$h$,$ calculate the magnitude of the normal force on the car from the road.

$5930$ N

$($b$)$ Calculate the maximum speed that the car can drive over the hill so that its wheels do not leave the road surface. Give the answer in km$/$h$.$

$82\mathrm{.}0$ km$/$h