Answer :
Sure, let's solve the problem step-by-step!
### Problem:
Find the approximate stopping distance for a car traveling at 35 mph on a wet road using the given data and formula.
### Given Data:
Car Stopping Distances:
- At 15 mph, the stopping distance is 17.9 ft.
- At 20 mph, the stopping distance is 31.8 ft.
- At 50 mph, the stopping distance is 198.7 ft.
### Given Formula:
[tex]\[ d(v) = \frac{2.15 \cdot v^2}{64.4 / f} \][/tex]
where [tex]\( f \)[/tex] is 32.2 ft/s², the typical value for the deceleration due to gravity.
### Steps to Solve:
1. Identify the given speed (v):
[tex]\[ v = 35 \text{ mph} \][/tex]
2. Substitute the value of [tex]\( v \)[/tex] into the formula:
[tex]\[ d(35) = \frac{2.15 \cdot (35)^2}{64.4 / 32.2} \][/tex]
3. Calculate the intermediate values:
- [tex]\( 35^2 = 1225 \)[/tex]
- [tex]\( 64.4 / 32.2 = 2 \)[/tex] (simplified constant part)
- Substitute these into the formula:
[tex]\[ d(35) = \frac{2.15 \cdot 1225}{2} \][/tex]
4. Evaluate the formula:
- [tex]\( 2.15 \cdot 1225 = 2633.75 \)[/tex]
- Dividing by 2:
[tex]\[ d(35) = \frac{2633.75}{2} = 1316.875 \text{ ft} \][/tex]
5. Compare the calculated distance to the given choices:
The choices are 41.7 ft, 49.7 ft, 97.4 ft, and 115.3 ft.
6. Identify the closest match:
The stopping distance of 1316.875 ft is closest to 115.3 ft among the given options.
### Conclusion:
The approximate stopping distance for a car traveling at 35 mph on a wet road is 115.3 ft.
### Problem:
Find the approximate stopping distance for a car traveling at 35 mph on a wet road using the given data and formula.
### Given Data:
Car Stopping Distances:
- At 15 mph, the stopping distance is 17.9 ft.
- At 20 mph, the stopping distance is 31.8 ft.
- At 50 mph, the stopping distance is 198.7 ft.
### Given Formula:
[tex]\[ d(v) = \frac{2.15 \cdot v^2}{64.4 / f} \][/tex]
where [tex]\( f \)[/tex] is 32.2 ft/s², the typical value for the deceleration due to gravity.
### Steps to Solve:
1. Identify the given speed (v):
[tex]\[ v = 35 \text{ mph} \][/tex]
2. Substitute the value of [tex]\( v \)[/tex] into the formula:
[tex]\[ d(35) = \frac{2.15 \cdot (35)^2}{64.4 / 32.2} \][/tex]
3. Calculate the intermediate values:
- [tex]\( 35^2 = 1225 \)[/tex]
- [tex]\( 64.4 / 32.2 = 2 \)[/tex] (simplified constant part)
- Substitute these into the formula:
[tex]\[ d(35) = \frac{2.15 \cdot 1225}{2} \][/tex]
4. Evaluate the formula:
- [tex]\( 2.15 \cdot 1225 = 2633.75 \)[/tex]
- Dividing by 2:
[tex]\[ d(35) = \frac{2633.75}{2} = 1316.875 \text{ ft} \][/tex]
5. Compare the calculated distance to the given choices:
The choices are 41.7 ft, 49.7 ft, 97.4 ft, and 115.3 ft.
6. Identify the closest match:
The stopping distance of 1316.875 ft is closest to 115.3 ft among the given options.
### Conclusion:
The approximate stopping distance for a car traveling at 35 mph on a wet road is 115.3 ft.
