When I was in high school, I often drove to Springfield from my home, and there was a curve in the road that was banked too steeply, so that if you went around it at 55 mph you actually felt like you were falling into the curve. I began experimenting to see how fast you needed to go to match the banking in the road, so that you didn't feel like you were tilting left or right as you went around. That portion of road was designed so that if the road was slippery your best chance at going around it without sliding was at 70 mph! I drove that road again recently, and sometime in the last 30 years they fixed it, reducing the bank to an angle appropriate for the speed limit. On the curve, banked at 24.5 ∘ from the horizontal, a car traveling at speed 19.0 m/s would still continue around the curve even with no friction.
What is the radius of the curve?
Express your answer using three significant figures.