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.
0.84
wrong 0.84
Hahah so easy took only 1 calculation consisting of 2 operation yeah yeah
To determine the angle at which the chicken should cross the road to maximize her chances of making it across without getting hit by a car, we need to consider the relative speed of the cars and the chicken's crossing speed.
Here's how we can approach this problem:
1. Calculate the time it takes for a car to reach the chicken after it crosses the road:
- Since the road is straight and the cars travel at a constant speed of 80 km/hr, the time it takes for a car to reach the chicken after it crosses the road is determined by the distance between the chicken and the road.
- Given that the cars have a log-normal distribution for their distances, we can determine the average distance between each car.
2. Calculate the time it takes for the chicken to cross the road:
- The chicken's crossing speed is given as 0.25 m/s.
- The width of the road is not explicitly mentioned, so let's assume it is denoted by 'w' units.
3. Determine the optimal crossing angle:
- The chicken should aim to minimize the time it spends on the road, which means maximizing the time period between cars.
- By maximizing the time period, the chicken increases the chances of reaching the other side of the road without getting hit.
- To maximize this time period, the chicken needs to choose an angle of crossing that aligns with the gap between consecutive cars.
4. Convert the optimal crossing angle to radians north of east:
- In the problem statement, it is mentioned that the road runs in the north-south direction.
- Therefore, the angle should be expressed in radians in relation to the east direction, which is perpendicular to the north-south axis.
By following these steps, we can determine the optimal crossing angle.