To determine the speed of the car based on the length of the skid marks, we can use the following formula which relates the speed (in miles per hour), the coefficient of friction, and the skid distance:
[tex]\[ v = \sqrt{30 \times f \times d} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed in miles per hour (mph),
- [tex]\( f \)[/tex] is the coefficient of friction,
- [tex]\( d \)[/tex] is the length of the skid marks in feet.
Given:
- The skid length ([tex]\( d \)[/tex]) is 48 feet,
- The coefficient of friction ([tex]\( f \)[/tex]) is 1.02.
Let's plug these values into the formula:
[tex]\[ v = \sqrt{30 \times 1.02 \times 48} \][/tex]
Calculating the product inside the square root first:
[tex]\[ 30 \times 1.02 = 30.6 \][/tex]
[tex]\[ 30.6 \times 48 = 1468.8 \][/tex]
Now, take the square root of 1468.8:
[tex]\[ v = \sqrt{1468.8} \approx 38.324926614411154 \][/tex]
Since speed is typically reported as an integer, we round the result to the nearest whole number:
[tex]\[ v \approx 38 \text{ mph} \][/tex]
So, the driver was going approximately 38 mph. Therefore, the correct answer is:
[tex]\[ \boxed{38 \text{ mph}} \][/tex]
