Police can estimate the speed of a vehicle before the breaks are applied using the formula 0.75d = s^2/30.25, where s is the speed in miles per hour and d is the length of the vehicle's skid marks. What was the approximate speed of a vehicle that left skid marks measuring 150 feet?
To find the approximate speed of the vehicle, we can rearrange the given formula:
0.75d = s^2/30.25
First, let's convert the length of the skid marks from feet to miles. Since 1 mile is equal to 5280 feet:
150 feet = 150/5280 miles ≈ 0.0284091 miles (rounded to 7 decimal places)
Substituting d = 0.0284091 into the formula:
0.75(0.0284091) = s^2/30.25
0.0213068 = s^2/30.25
Next, multiply both sides of the equation by 30.25 to isolate s:
s^2 = 0.0213068 * 30.25
s^2 ≈ 0.64469621 (rounded to 8 decimal places)
To find the value of s, we take the square root of both sides:
s ≈ √(0.64469621)
s ≈ 0.80293065
Finally, we round the speed to the nearest whole number:
The approximate speed of the vehicle was 1 mile per hour.