A car going 50mi/h overtakes and passes another car moving at 45 mi/h. what length of road is required for the operation? assume that each car is 15 ft long and that there is a 60-ft space between them before and after passing. taking into account the approach of a car from the opposite direction at 50 mi/h, what clear length of road is required?
One car passes the other at a relative rate of 5 mph = 7.333 ft/s, and must change the distance between them by 60 + 60 + 15 = 135 feet before returning to the right side of the dividing line. The time required for the entire passing maneuver is 135/7.333 = 18.41 s. An oncoming car approaches the passing car at a relative rate 100 mph = 146.7 ft/s. The clear length of road required to avoid a collision is
146.7 x 18.41 = 2700 feet, which is over half a mile.
12
To calculate the length of road required for the overtaking maneuver, we need to consider the length of both cars, the space between them, and the distance traveled during the passing operation.
Given:
- The speed of the overtaking car is 50 mph.
- The speed of the car being passed is 45 mph.
- The length of each car is 15 ft.
- There is a 60 ft space between the cars before and after passing.
First, let's find the distance traveled by both cars during the passing maneuver.
Since both cars are moving at different speeds, the relative speed of the overtaking car to the car being passed is the difference between their speeds: 50 mph - 45 mph = 5 mph.
To convert the relative speed to feet per hour:
5 mph * 5280 ft/mi = 26,400 ft/h.
Now, let's calculate the time it takes to cover the distance between the cars.
Distance = Relative Speed * Time
We want to find the time it takes for the overtaking car to cover the sum of both car lengths and the space between them, which is 15 ft + 15 ft + 60 ft = 90 ft.
90 ft = 26,400 ft/h * Time
Solving for Time:
Time = 90 ft / (26,400 ft/h)
Time ≈ 0.00341 hours
Now, let's calculate the distance the overtaking car will travel during this time.
Distance = Speed * Time
Distance = 50 mph * 0.00341 hours
Distance ≈ 0.1705 miles
Therefore, the length of road required to complete the overtaking maneuver is approximately 0.1705 miles.
However, we also need to consider the approach of a car from the opposite direction at 50 mph.
Since each car is 15 ft long and there is a 60 ft space between them, the total length of the cars and space is 2 * (15 ft + 60 ft) = 150 ft.
To calculate the minimum clear length of road required, we need to treat the overtaking and approaching cars as if they were traveling in opposite directions and compute the distance needed for both to pass safely.
Starting with the distance traveled by the overtaking car:
Distance_overtaking = 50 mph * 0.00341 hours ≈ 0.1705 miles
The distance traveled by the approaching car will also be 0.1705 miles since they're approaching head-on and will meet at the average of their speeds.
Adding both distances:
Total distance = 0.1705 miles + 0.1705 miles = 0.341 miles
Therefore, the total clear length of road required for both cars to pass safely is approximately 0.341 miles.
To determine the length of road required for the overtaking operation, we need to calculate the total distance traveled by the overtaking car while passing the other car.
Step 1: Convert the speeds from miles per hour to feet per second.
- Car going 50 mi/h: 50 * 5280 ft / 3600 s ≈ 73.33 ft/s
- Car going 45 mi/h: 45 * 5280 ft / 3600 s ≈ 66 ft/s
Step 2: Calculate the time it takes for the overtaking car to pass the other car.
We know that the relative speed of the overtaking car is the sum of their speeds:
Relative speed = 73.33 ft/s - 66 ft/s = 7.33 ft/s
The length of the two cars (15 ft each) and the space between them (60 ft before and after passing) adds up to 15 ft + 15 ft + 60 ft + 60 ft = 150 ft.
Time = Distance / Speed
Passing time = 150 ft / 7.33 ft/s ≈ 20.48 seconds
Step 3: Calculate the distance traveled by the overtaking car during the passing time.
Distance = Speed * Time
Distance = 73.33 ft/s * 20.48 s ≈ 1500 ft
Therefore, the length of road required for the overtaking operation is approximately 1500 feet.
Now, let's consider the approach of a car from the opposite direction at 50 mi/h.
Step 4: Calculate the time it takes for the approaching car to reach the passing point.
The relative speed of the two cars is the sum of their speeds:
Relative speed = 73.33 ft/s + 66 ft/s = 139.33 ft/s
Time = Distance / Speed
Approaching time = 150 ft / 139.33 ft/s ≈ 1.08 seconds
Step 5: Calculate the distance traveled by the overtaking car during the approaching time.
Distance = Speed * Time
Distance = 66 ft/s * 1.08 s ≈ 71.28 ft
Therefore, taking into account the approach of a car from the opposite direction at 50 mi/h, the clear length of road required is approximately 71.28 feet.