How did the chicken cross the road?

Classical Mechanics Level 4

A chicken decides to cross a road. The road is perfectly straight, runs north-south, and is full of cars driving by from south to north. The cars have a log-normal distribution for the distance between each car. However, the cars all travel at 80 km/hr.

The chicken stands next to the road on the west side, waits until a car goes by, and then immediately starts to cross the road at 0.25 m/s. What angle should the chicken cross at to maximize her chance of making it across the road without getting hit by a car? Express your answer as radians north of east.

Details and assumptions

  • The chicken is a point particle.
  • Assume for simplicity that a car is the same width as the road, so that if the chicken is on the road when the car reaches her, she gets hit.

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