1. The problem statement, all variables and given/known data A race boat is traveling at a constant speed v0 = 130 mph when it performs a turn with constant radius ρ to change its course by 90°. The turn is performed while losing speed uniformly in time so that the boat's speed at the end of the turn is vf = 116 mph. If the magnitude of the acceleration is not allowed to exceed 2g, where g is the acceleration due to gravity, determine the tightest radius of curvature possible and the time needed to complete the turn. 2. Relevant equations ρ(x) = ([1 + (dy/dx)2]3/2)/(absvalue(d2y/dx2)) *edit* an = v2/ρ a = atut + anun v = vut at t = 0; ut = -sin90i + cos90j 3. The attempt at a solution So the distance traveled by the boat is 1/4 of a circle, s = rθ = ρ([itex]\pi[/itex]/2) converting mph to ft / s v2 = v02 + 2 ac(s - s0) [(170.13)2 - (190.67)2] / 2(32.2 ft/ s ^2) = s s = 57.5 ft = 17.5 meters ρ = 57.5 ft * 2 / pi I feel like I'm missing something BIG because it can't be this simple.