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------------------------------------------------ The table below shows the data for a car stopping on a wet road. What is the approximate stopping distance for a car traveling 35 mph?

**Car Stopping Distances**

[tex]
\[
\begin{tabular}{|c|c|}
\hline
v & d \\
\hline
(\text{mph}) & (\text{ft}) \\
\hline
15 & 17.9 \\
\hline
20 & 31.8 \\
\hline
50 & 198.7 \\
\hline
\end{tabular}
\]
[/tex]

[tex]
d(v) = \frac{2.15 v^2}{64.4 f}
[/tex]

A. 41.7 ft
B. 49.7 ft
C. 97.4 ft
D. 195.26 ft

Answer :

To find the stopping distance for a car traveling at 35 mph on a wet road, we can use a formula that considers factors like the speed of the car and the friction of the road. The formula looks like this:

[tex]\[ o(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]

Where:
- [tex]\( v \)[/tex] is the vehicle's speed in miles per hour (mph).
- [tex]\( f \)[/tex] is the friction coefficient representing the grip between the tires and the wet road. For wet roads, a typical friction value is around 0.7.

Let's calculate the stopping distance step-by-step:

1. Determine known values:
- The speed [tex]\( v \)[/tex] is 35 mph.
- The friction coefficient [tex]\( f \)[/tex] is 0.7.

2. Plug these values into the formula:

[tex]\[
o(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]

3. Calculate the numerator:
- [tex]\( 35^2 = 1225 \)[/tex]
- [tex]\( 2.15 \times 1225 = 2633.75 \)[/tex]

4. Calculate the denominator:
- [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex]

5. Perform the division to find the stopping distance:

[tex]\[
\text{Stopping distance} = \frac{2633.75}{45.08} \approx 58.42
\][/tex]

Therefore, the stopping distance for a car traveling at 35 mph on a wet road is approximately 58.42 feet.