Answer :
To find the approximate stopping distance for a car traveling at 35 mph on a wet road, we can use the stopping distance formula:
[tex]\[ q(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
Here, [tex]\( v \)[/tex] is the speed of the car in miles per hour and [tex]\( f \)[/tex] is the coefficient of friction, which we'll assume is 1 for simplification.
1. Plug in the value of [tex]\( v \)[/tex]:
We have [tex]\( v = 35 \)[/tex] mph.
2. Assume the coefficient of friction [tex]\( f \)[/tex] is 1:
This simplification means we assume normal wet road conditions where the coefficient of friction doesn't add more complexity.
3. Calculate the stopping distance:
Substitute [tex]\( v = 35 \)[/tex] and [tex]\( f = 1 \)[/tex] into the formula:
[tex]\[
q(35) = \frac{2.15 \times 35^2}{64.4 \times 1}
\][/tex]
Simplify the calculation:
[tex]\[
q(35) = \frac{2.15 \times 1225}{64.4}
\][/tex]
[tex]\[
q(35) = \frac{2637.5}{64.4}
\][/tex]
[tex]\[
q(35) \approx 40.90
\][/tex]
Therefore, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 40.9 feet. This does not match any provided option exactly, but it is closest to 41.7 feet, suggesting 41.7 feet would be the best choice given the options available.
[tex]\[ q(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
Here, [tex]\( v \)[/tex] is the speed of the car in miles per hour and [tex]\( f \)[/tex] is the coefficient of friction, which we'll assume is 1 for simplification.
1. Plug in the value of [tex]\( v \)[/tex]:
We have [tex]\( v = 35 \)[/tex] mph.
2. Assume the coefficient of friction [tex]\( f \)[/tex] is 1:
This simplification means we assume normal wet road conditions where the coefficient of friction doesn't add more complexity.
3. Calculate the stopping distance:
Substitute [tex]\( v = 35 \)[/tex] and [tex]\( f = 1 \)[/tex] into the formula:
[tex]\[
q(35) = \frac{2.15 \times 35^2}{64.4 \times 1}
\][/tex]
Simplify the calculation:
[tex]\[
q(35) = \frac{2.15 \times 1225}{64.4}
\][/tex]
[tex]\[
q(35) = \frac{2637.5}{64.4}
\][/tex]
[tex]\[
q(35) \approx 40.90
\][/tex]
Therefore, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 40.9 feet. This does not match any provided option exactly, but it is closest to 41.7 feet, suggesting 41.7 feet would be the best choice given the options available.
