Type your answer If a car is driving up a hill at 50 miles per hour along an angle of $$ 10^{\circ} $$, what is the car's vertical speed? (Note: $$ \sin \left(10^{\circ}\right) \approx 0.17 $$ and $$ \cos \left(10^{\circ}\right) \approx 0.98 $$ )

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To determine the car's **vertical speed** while driving up a hill, we can use the following approach:

1. **Understand the Components:**
   - The car's speed along the hill (the **hypotenuse** of the right triangle) is **50 miles per hour**.
   - The hill's incline angle is $$10^{\circ}$$.

2. **Vertical Component Calculation:**
   - The **vertical speed** is the component of the car's velocity in the direction perpendicular to the horizontal plane.
   - This can be calculated using the sine function:
     $$
     \text{Vertical Speed} = \text{Speed} \times \sin(\theta)
     $$
     where $$\theta = 10^{\circ}$$.

3. **Plug in the Values:**
   $$
   \text{Vertical Speed} = 50 \, \text{mph} \times \sin(10^{\circ}) \approx 50 \, \text{mph} \times 0.17 = 8.5 \, \text{mph}
   $$

**Conclusion:**
The car's vertical speed is **approximately 8.5 miles per hour**.
The car's vertical speed is approximately 8.5 miles per hour.

Type your answer If a car is driving up a hill at 50 miles per hour along an angle of \( 10^{\circ} \), what is the car's vertical speed? (Note: \( \sin \left(10^{\circ}\right) \approx 0.17 \) and \( \cos \left(10^{\circ}\right) \approx 0.98 \) )

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