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.
[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.
