An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the necessary force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. Show that for a given speed v and a radius of r , the curve must be banked at the angle (theta) such that tan(theta)=v^2/r*g
What have you tried? think about what tan(theta) is in terms of sine and cosine and what sine and cosine would represent in this case.
this is what i was thinking... Fn sin(theta) = mv^2/r (mg/cos(theta))sin(theta) = mg tan(theta) = mv^2/r tan theta = v^2/(rg) does that look right?