Find the final velocity at ground level and at 6% grade separately

To find the final velocity at ground level (0% grade) and at a 6% grade separately, we'll follow a similar process as before, adjusting the slope angle accordingly:

### Ground Level (0% Grade)
For ground level, the slope angle \( \theta \) is 0°, so the gravitational component \( F_g \) is zero, and we only consider rolling resistance and aerodynamic drag.

### 6% Grade
For a 6% grade, the slope angle \( \theta \) corresponds to the arctangent of 0.06. We then include the gravitational force component, rolling resistance, and aerodynamic drag in the calculation.

### Equations Recap
1. **Aerodynamic Drag Force \( F_D \):**
\[
F_D = \frac{1}{2} \times \text{Density} \times \text{CD} \times \text{AF} \times V^2
\]

2. **Gravitational Force \( F_g \):**
\[
F_g = W \times \sin(\theta)
\]

3. **Rolling Resistance \( F_{rr} \):**
\[
F_{rr} = \mu \times W \times \cos(\theta)
\]

4. **Final Velocity \( V_f \) Equation:**
\[
W \times Yb = F_{rr} + F_D + F_g
\]

Now let's calculate the final velocities for both cases.The final velocities are as follows:

- **Ground level (0% grade):** \( V_f \approx 112.93 \, \text{m/s} \)
- **6% grade:** \( V_f \approx 107.41 \, \text{m/s} \)

Would you like more details or have any further questions?

Here are five related questions you might consider:
1. What effect does increasing the grade percentage have on final velocity?
2. How would a change in rolling resistance \( \mu \) impact these results?
3. What would be the final velocity at a negative slope (downhill)?
4. How would the final velocity change if the weight \( W \) were different?
5. What role does the tractive force coefficient \( Yb \) play in determining the final velocity?

**Tip:** The slope of the road has a significant impact on the final velocity due to the additional gravitational force component on inclined planes.

Learn how to calculate final velocity at ground level (0% grade) and at a 6% grade using physics principles. This problem covers aerodynamic drag, gravitational force, rolling resistance, and the final velocity equation. Suitable for advanced high school and college-level students.

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