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Answer :
To find the approximate stopping distance for a car traveling at 35 mph on a wet road, we can use the provided formula for stopping distance:
[tex]\[ d(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed in miles per hour (mph),
- [tex]\( f \)[/tex] is the average friction coefficient for a wet road.
In this case, the average friction coefficient for a wet road is typically around 0.7. Now, let's go through the steps:
1. Identify the speed ([tex]\( v \)[/tex]):
- The problem states the car is traveling at [tex]\( v = 35 \)[/tex] mph.
2. Use the friction coefficient ([tex]\( f \)[/tex]):
- We are using [tex]\( f = 0.7 \)[/tex].
3. Insert these values into the formula:
[tex]\[
d(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]
4. Perform the calculations:
- First, calculate the square of the speed: [tex]\( 35^2 = 1225 \)[/tex].
- Then, multiply by 2.15: [tex]\( 2.15 \times 1225 = 2633.75 \)[/tex].
- Calculate the denominator: [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex].
- Finally, divide the results: [tex]\( \frac{2633.75}{45.08} \approx 58.42 \)[/tex].
Therefore, the approximate stopping distance for a car traveling 35 mph on a wet road is about 58.4 feet.
[tex]\[ d(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed in miles per hour (mph),
- [tex]\( f \)[/tex] is the average friction coefficient for a wet road.
In this case, the average friction coefficient for a wet road is typically around 0.7. Now, let's go through the steps:
1. Identify the speed ([tex]\( v \)[/tex]):
- The problem states the car is traveling at [tex]\( v = 35 \)[/tex] mph.
2. Use the friction coefficient ([tex]\( f \)[/tex]):
- We are using [tex]\( f = 0.7 \)[/tex].
3. Insert these values into the formula:
[tex]\[
d(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]
4. Perform the calculations:
- First, calculate the square of the speed: [tex]\( 35^2 = 1225 \)[/tex].
- Then, multiply by 2.15: [tex]\( 2.15 \times 1225 = 2633.75 \)[/tex].
- Calculate the denominator: [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex].
- Finally, divide the results: [tex]\( \frac{2633.75}{45.08} \approx 58.42 \)[/tex].
Therefore, the approximate stopping distance for a car traveling 35 mph on a wet road is about 58.4 feet.
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