When a car makes an emergency stop on dry pavement, it leaves skid marks on the pavement. The speed S, in miles per hour, of the car when the brakes were applied is related to the length L, in feet, of the skid mark. The relationship is S(L) = 5.05 square root L. Calculate the speed of a car that leaves a 70 food skid mark.

To calculate the speed \( S \) of a car that leaves a 70-foot skid mark, we can use the given relationship:

\[
S(L) = 5.05 \times \sqrt{L}
\]

where \( L \) is the length of the skid mark in feet. Plugging in \( L = 70 \) feet:

\[
S(70) = 5.05 \times \sqrt{70}
\]

Now, calculate the square root of 70:

\[
\sqrt{70} \approx 8.37
\]

Then, multiply by 5.05:

\[
S(70) = 5.05 \times 8.37 \approx 42.26 \text{ miles per hour}
\]

So, the speed of the car was approximately **42.26 miles per hour**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions:
1. What would be the speed if the skid mark was 100 feet long?
2. How does the speed change if the length of the skid mark doubles?
3. What is the physical significance of the constant 5.05 in the equation?
4. If a car stops on wet pavement, would you expect the constant in the formula to be higher or lower?
5. How could you use this formula in a real-world investigation of a car accident?

**Tip:** When dealing with square roots in formulas, ensure the units of measurement are consistent to avoid errors.

Learn how to calculate the speed of a car based on the length of its skid mark using the formula S(L) = 5.05 * sqrt(L). This problem explores the relationship between car speed and skid mark length, providing a practical application of square roots and linear relationships in physics. Suitable for high school students.

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