The headlights on a car are set so the light beam drops 2 in. for each 21 ft measured horizontally. If the headlights are mounted 28 in. above the​ ground, how far ahead of the car will they hit the​ ground?
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Part 1
The light beam will hit the ground at a distance of

enter your response here ft ahead of the car.
​(Simplify your​ answer)

We are given that the headlights drop 2 inches for every 21 feet measured horizontally and the headlights are mounted 28 inches above the ground. The question asks how far ahead the headlights will hit the ground.

This problem can be modeled as a linear relationship between the drop in height and the horizontal distance.

The key steps to solve the problem are:

1. **Find the slope of the light beam:**
   The drop per horizontal distance is 2 inches for every 21 feet. So, the slope of the line is:
   \[
   \text{slope} = \frac{2 \text{ inches}}{21 \text{ feet}}.
   \]
   
   Convert the 21 feet into inches:
   \[
   21 \text{ feet} = 21 \times 12 = 252 \text{ inches}.
   \]
   
   So, the slope becomes:
   \[
   \text{slope} = \frac{2}{252} = \frac{1}{126}.
   \]
   
   This means that for every 126 inches horizontally, the light beam drops by 1 inch.

2. **Set up the equation for the total drop:**
   The total vertical drop of the light beam is 28 inches (the height of the headlights above the ground). Let \( x \) be the horizontal distance (in inches) where the beam hits the ground. 

   Since the slope is \( \frac{1}{126} \), we can set up the equation:
   \[
   \frac{1}{126} \times x = 28.
   \]

3. **Solve for \( x \):**
   \[
   x = 28 \times 126 = 3528 \text{ inches}.
   \]

4. **Convert \( x \) to feet:**
   \[
   x = \frac{3528}{12} = 294 \text{ feet}.
   \]

Therefore, the light beam will hit the ground **294 feet** ahead of the car.

Would you like more details on any of the steps? Here are some related questions to consider:

1. How would the solution change if the headlights were mounted at a different height?
2. How would the slope change if the beam dropped 3 inches for every 21 feet?
3. What is the significance of the slope in real-world applications?
4. How can we represent this scenario graphically?
5. How do the units (inches and feet) affect the calculation?

**Tip:** Always ensure that units are consistent when solving real-world problems. Converting all measurements to the same unit at the start makes the math much easier!

The headlights on a car are set so the light beam drops 2 in. for each 21 ft measured horizontally. If the headlights are mounted 28 in. above the ground, how far ahead of the car will they hit the ground?

Learn how to calculate the distance where a car's headlights, mounted 28 inches above the ground, will hit the ground if the light beam drops 2 inches for every 21 feet. This problem involves linear relationships, unit conversions, and slope calculations. Suitable for students in Grades 9-11.

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