Answer :
Answer:
To solve this problem, we need to calculate the theoretical stopping distance and compare it to the actual stopping distance to find the braking efficiency.
Given information:
- Initial speed: 90 mi/h
- Grade: 3% (downhill)
- Pavement condition: wet
- Skid marks: 410 ft
- Impact speed: 45 mi/h
Step 1: Convert the speeds to ft/s.
Initial speed: 90 mi/h = 132 ft/s
Impact speed: 45 mi/h = 66 ft/s
Step 2: Calculate the theoretical stopping distance.
The theoretical stopping distance can be calculated using the formula:
Theoretical stopping distance = (v^2) / (2 * g * (μ ± sin(θ)))
Where:
- v = initial speed (ft/s)
- g = acceleration due to gravity (32.2 ft/s²)
- μ = coefficient of friction (wet pavement = 0.35)
- θ = angle of the grade (3% = 1.7 degrees)
Theoretical stopping distance = (132^2) / (2 * 32.2 * (0.35 - sin(1.7°)))
Theoretical stopping distance = 618 ft
Step 3: Calculate the braking efficiency.
Braking efficiency = (Theoretical stopping distance - Actual stopping distance) / Theoretical stopping distance
Braking efficiency = (618 ft - 410 ft) / 618 ft
Braking efficiency = 0.334 or 33.4%
Therefore, the braking efficiency of the car was 33.4%.
