A car skidded on a roadway that has a coefficient of friction with the road of 0.7. A police officer measured the skid marks and noted them to be 100 feet long. Two years later at trial, the lawyer for the driver argues that the officer did not measure the skid marks correctly. He asserts, based on photographs, that skid marks were no more than 92 feet long. Is the difference significant?

Assuming the car came to a stop..

vf^2=vi^2+ 2ad=vi^2 - 2 mu*g*d

vi=sqrt (2mu*g*d)

so the question is what is the ratio of
sqrt(92/100)?

well, at 92, vi kwould have been 96 percent of what the officer orginally estimated. Probably not significant.

To determine if the difference in skid mark lengths is significant, we need to calculate the range of possible values based on the given coefficient of friction and assess whether the observed value falls within that range. Here's how we can do that:

1. Calculate the range of possible skid mark lengths:
- The coefficient of friction (μ) between the car's tires and the road is given as 0.7.
- The formula to calculate the skid mark length (S) is: S = (v^2 / (30 * μ * g)), where v is the initial velocity of the car before skidding and g is the acceleration due to gravity (approximately 32.2 ft/s^2).
- Rearranging the formula, we get: v = sqrt(S * 30 * μ * g).
- Let's calculate the range of initial velocities that could produce a skid mark length between 92 and 100 feet.
- For an S value of 92 feet: v = sqrt(92 * 30 * 0.7 * 32.2).
- For an S value of 100 feet: v = sqrt(100 * 30 * 0.7 * 32.2).
- Calculate these values using a scientific calculator or software.

2. Compare the observed skid mark length:
- If the observed skid mark length of 100 feet falls within the range of possible values, then the argument made by the lawyer for the driver is not significant. However, if it falls outside the calculated range, it would be worth further investigation.

By following these steps, you will be able to determine whether the difference in skid mark lengths is significant or not based on the given coefficient of friction.