Asked by Daphne Scotese on Jul 16, 2024
Verified
Craig is an accident reconstructionist.He arrives at an accident where there are 4 skid marks of different lengths.He finds their measures to be 85 ft,92 ft,88 ft,and 90 ft.It is an asphalt road with a drag factor of 0.8.Because he does not know the efficiency of the driver's brakes,he assumes a brake efficiency of 80%.What is the minimum speed the driver could have been going?
A) 31.6 mph
B) 38.2 mph
C) 41.3 mph
D) 46.2 mph
Accident Reconstructionist
Person with knowledge of both crime scene investigations and the mathematics that can help to explain the circumstances surrounding the accident.
Skid Marks
Visible marks left on the road surface by tires that have slipped or skidded, often analyzed in accident reconstructions.
Drag Factor
A coefficient used in calculating the deceleration or resistance force acting against a moving object or vehicle, often in automotive and aeronautical engineering.
- Compute the velocities of vehicles by analyzing skid marks and friction coefficients.
Verified Answer
MD
maryse denejusteJul 16, 2024
Final Answer :
C
Explanation :
To find the minimum speed the driver could have been going, we need to use the formula:
v = (d / (1.47 * sqrt(f * e)))
Where:
- v is the initial speed of the vehicle in mph
- d is the length of the skid marks in feet
- f is the drag factor of the road surface (0.8 in this case)
- e is the brake efficiency (80% = 0.8)
We can use this formula for each skid mark length and take the lowest speed as the minimum speed the driver could have been going:
For 85 ft: v = (85 / (1.47 * sqrt(0.8 * 0.8))) = 31.6 mph
For 92 ft: v = (92 / (1.47 * sqrt(0.8 * 0.8))) = 34.7 mph
For 88 ft: v = (88 / (1.47 * sqrt(0.8 * 0.8))) = 32.9 mph
For 90 ft: v = (90 / (1.47 * sqrt(0.8 * 0.8))) = 33.6 mph
The lowest speed is therefore 31.6 mph, which corresponds to choice C.
v = (d / (1.47 * sqrt(f * e)))
Where:
- v is the initial speed of the vehicle in mph
- d is the length of the skid marks in feet
- f is the drag factor of the road surface (0.8 in this case)
- e is the brake efficiency (80% = 0.8)
We can use this formula for each skid mark length and take the lowest speed as the minimum speed the driver could have been going:
For 85 ft: v = (85 / (1.47 * sqrt(0.8 * 0.8))) = 31.6 mph
For 92 ft: v = (92 / (1.47 * sqrt(0.8 * 0.8))) = 34.7 mph
For 88 ft: v = (88 / (1.47 * sqrt(0.8 * 0.8))) = 32.9 mph
For 90 ft: v = (90 / (1.47 * sqrt(0.8 * 0.8))) = 33.6 mph
The lowest speed is therefore 31.6 mph, which corresponds to choice C.
Learning Objectives
- Compute the velocities of vehicles by analyzing skid marks and friction coefficients.