A driver is traveling at 90 mi/h down a 3% grade on good, wet pavement. An accident investigation team noted that braking skid marks started 410 ft before a parked car was hit at an estimated 45 mi/h. Ignoring air resistance, and using theoretical stopping distance, what was the braking efficiency of the car.



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%.