To anticipate the dip and hump in the road, the driver of a car applies her brakes to produce a uniform deceleration. Her speed is \(100 \mathrm{~km} / \mathrm{h}\) at the bottom \(A\) of the dip and \(50 \mathrm{~km} / \mathrm{h}\) at the top \(C\) of the hump, which is \(120 \mathrm{~m}\) along the road from \(A\). If the passengers experience a total acceleration of \(3 \mathrm{~m} / \mathrm{s}^{2}\) at \(A\) and if the radius of curvature of the hump at \(C\) is \(150 \mathrm{~m}\), calculate \((a)\) the radius of curvature \(ho\) at \(A,(b)\) the acceleration at the inflection point \(B\), and \((c)\) the total acceleration at \(C\).

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B