Human reaction times are worsened by alcohol. How much farther would a drunk driver's car travel before he hits the brakes than a sober driver's car? Assume both cars are initially traveling at 47.0 mi/h, the sober driver takes .33 s and the drunk driver takes 1.0 s to hit the brakes in a crisis.
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First, we need to convert the speed from miles per hour (mi/h) to feet per second (ft/s). We can do this by knowing that there are 5280 feet in a mile and 3600 seconds in an hour:
47.0 mi/h * (5280 ft/mi) / (3600 s/h) = 68.8 ft/s
Now, we need to find the distance each car travels during the reaction time.
For the sober driver with a reaction time of 0.33 s:
Distance_sober = Speed × Time
Distance_sober = 68.8 ft/s × 0.33 s
Distance_sober ≈ 22.7 feet
For the drunk driver with a reaction time of 1.0 s:
Distance_drunk = Speed × Time
Distance_drunk = 68.8 ft/s × 1.0 s
Distance_drunk = 68.8 feet
Now we can find the difference between these distances:
Difference = Distance_drunk - Distance_sober
Difference = 68.8 ft - 22.7 ft
Difference ≈ 46.1 feet
So a drunk driver's car would travel about 46.1 feet farther before he hits the brakes than a sober driver's car.
To calculate how much farther a drunk driver's car would travel before hitting the brakes compared to a sober driver's car, we first need to find the distance each car would travel before stopping.
1. Convert the initial speed from miles per hour (mi/h) to feet per second (ft/s):
- 47.0 mi/h * (5280 ft/mi) / (3600 s/h) = 68.9333 ft/s
- The initial speed of both cars is 68.9333 ft/s.
2. Calculate the distance traveled by the sober driver's car:
- Distance = Speed * Time
- Distance = 68.9333 ft/s * 0.33 s = 22.765 ft
- The sober driver's car would travel a distance of 22.765 ft before hitting the brakes.
3. Calculate the distance traveled by the drunk driver's car:
- Distance = Speed * Time
- Distance = 68.9333 ft/s * 1.0 s = 68.9333 ft
- The drunk driver's car would travel a distance of 68.9333 ft before hitting the brakes.
4. Calculate the difference in distance traveled:
- Difference = Distance (drunk driver) - Distance (sober driver)
- Difference = 68.9333 ft - 22.765 ft = 46.1683 ft
Therefore, the drunk driver's car would travel approximately 46.1683 feet farther before hitting the brakes compared to the sober driver's car.
To determine the difference in distance traveled by the cars before hitting the brakes, we need to calculate the distance each car would travel during their respective reaction times.
First, let's convert the initial velocity of 47.0 mi/h to feet per second (ft/s) since we will be working with time in seconds:
1 mile = 5280 feet
1 hour = 3600 seconds
So, 47.0 mi/h = (47.0 * 5280 ft) / (1 * 3600 s) = 68.933 ft/s (rounded to three decimal places).
Now, let's find the distance traveled by the sober driver's car during the reaction time of 0.33 seconds:
Distance = Velocity * Time
Distance = 68.933 ft/s * 0.33 s = 22.749 ft (rounded to three decimal places).
The sober driver's car would travel approximately 22.749 feet before hitting the brakes.
Next, let's find the distance traveled by the drunk driver's car during the longer reaction time of 1.0 second:
Distance = Velocity * Time
Distance = 68.933 ft/s * 1.0 s = 68.933 ft.
The drunk driver's car would travel approximately 68.933 feet before hitting the brakes.
To find the difference in distance traveled between the two cars, we subtract the distance traveled by the sober driver's car from the distance traveled by the drunk driver's car:
Difference in distance = Distance of drunk driver - Distance of sober driver
Difference in distance = 68.933 ft - 22.749 ft = 46.184 ft (rounded to three decimal places).
Therefore, a drunk driver's car would travel approximately 46.184 feet farther than a sober driver's car before hitting the brakes in a crisis.