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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**

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

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

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

Answer :

To determine the approximate stopping distance for a car traveling at 35 mph on a wet road, we can use the provided formula:

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

Here, [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph), and [tex]\( f \)[/tex] is the coefficient of friction. For standard wet conditions, the coefficient of friction [tex]\( f \)[/tex] is typically around 0.7.

Let's substitute the given values into the formula:

1. [tex]\( v = 35 \)[/tex] mph
2. [tex]\( f = 0.7 \)[/tex]

Now, we can calculate the stopping distance [tex]\( d \)[/tex]:

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

First, calculate [tex]\( 35^2 \)[/tex]:

[tex]\[ 35^2 = 1225 \][/tex]

Next, multiply by 2.15:

[tex]\[ 2.15 \times 1225 = 2637.5 \][/tex]

Then, multiply [tex]\( 64.4 \)[/tex] by [tex]\( 0.7 \)[/tex]:

[tex]\[ 64.4 \times 0.7 = 45.08 \][/tex]

Now, divide the result from the numerator by the result from the denominator:

[tex]\[ \frac{2637.5}{45.08} \approx 58.42 \][/tex]

So, the approximate stopping distance for a car traveling at 35 mph on a wet road is:

[tex]\[ \boxed{58.42 \text{ ft}} \][/tex]