As you travel every day to campus, the road makes a large turn thatis approximately an arc of a circle. You notice the warning sign atthe start of the turn, asking for a maximum speed of 55 \rm{mi/h}. You also notice that in the curved portion theroad is level-that is, not banked at all. On a dry day with verylittle traffic, you enter the turn at a constant speed of 80\rm{mi/h} and feel that the car may skid if you do not slowdown quickly. You conclude that your speed is at the limit ofsafety for this curve and you slow down. However, you rememberreading that on dry pavement new tires have an average coefficientof static friction of about 0.76, while under the worst winterdriving conditions, you may encounter wet ice for which thecoefficient of static friction can be as low as 0.20. Wet ice isnot unheard of on this road, so you ask yourself whether the speedlimit for the turn on the roadside warning sign is for theworst-case scenario. Estimate the radius of the curve from your 80\rm{mi/h} experience in the dry turn. Use this estimate to find the maximum speedlimit in the turn under the worst wet-ice conditions. How does this compare with the speed limit onthe sign? Is the sign misleading drivers? On a rainy day, the coefficient of staticfriction would be about 0.37. What is the maximum safe speed forthe turn when the road is wet?