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]
[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]
