College

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

**Car Stopping Distances**

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

Using the formula: [tex]d(v)=\frac{2.15 v^2}{64.4}[/tex]

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

Answer :

Sure, let's find the approximate stopping distance for a car traveling at 35 mph on a wet road using the provided formula:

The formula given for the stopping distance [tex]\( d(v) \)[/tex] is:

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

Where:
- [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph).
- [tex]\( f \)[/tex] is the coefficient of friction, which is provided as 0.7 for a wet road.

Let's break down the steps to calculate the stopping distance:

1. Identify the values:
- Speed ([tex]\( v \)[/tex]) = 35 mph
- Friction factor ([tex]\( f \)[/tex]) = 0.7

2. Plug in the values into the formula:

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

3. Calculate [tex]\( (35)^2 \)[/tex]:

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

4. Multiply by the constant 2.15:

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

5. Calculate the denominator:

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

6. Divide the result from step 4 by the result from step 5:

[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 about 58.42 feet.