The highway ramp shown below (not to scale) produces a 180 degree turn in the ro
ID: 1333363 • Letter: T
Question
The highway ramp shown below (not to scale) produces a 180 degree turn in the road, as well as moving between elevated and ground-level road sections. In cylindrical coordinates with origin O, a car driving on the ramp has a constant distance R = 30 m from the z axis and a height z given as a function of the angle theta by z(theta) = 7(1 - cos theta) m. We assume that the car is a point mass, and the figure does not show the car in the correct location. What is the difference between the radius of curvature rho of the car's path and the distance R when theta = 42 degree?Explanation / Answer
From pythagorian theorem,R2=p2+z2; when angle=42,
p=27.4m
p-R=-2.59m
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