CSI Challenge: Car on the off ramp

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CASE FILE: Overturned Automobile

Intro:

Mr. Montoya’s car was found off the side of a highway on-ramp, overturned and well off the road on the night of the twenty-second. Luckily, no one was injured in the accident but the car was totaled pretty badly.

Problem Statement:

The road on the ramp from which the car slid off was banked on a circular arc at 30 degrees. Distance from the middle of the road to the center of the arc was measured at 19.3 meters. The speed limit was posted at 30 mph and Mr. Montoya claims he was driving at the exact speed limit. Mr. Montoya now claims that the speed limit is set much too high for the curve of the turn it’s suspected that Mr. Montoya was really driving above the speed limit and that’s what caused the crash.

Potential Scenarios:

• The speed limit is set too high; 30 mph is too fast to stay on the road

• Mr. Montoya’s car was slid off the road because he was speeding

Background:

Distance from middle of road to center of circular arc: 19.3 m

Bank of curve: 30 degrees

Speed Limit: 30 mph

Coefficient of asphalt: .9

30 mph = 13.4112 m/s

Assignment:

Determine the maximum velocity a car should be able to make the turn to determine if Mr. Montoya was speeding or the speed limit is inappropriate for the turn.

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