A man applies a constant horizontal force of 64.9 N to a box sitting on an incline of 38.1 degrees. If he does 493.1 J of work, how far along the ramp did he push the box? (please provide your answer to 1 decimal place)

To determine the distance along the ramp the man pushed the box, we can use the work-energy principle, which states that work \( W \) is given by the formula:

\[
W = F \cdot d \cdot \cos(\theta)
\]

Where:
- \( W \) is the work done (493.1 J),
- \( F \) is the horizontal force applied (64.9 N),
- \( d \) is the distance along the ramp (what we are trying to find),
- \( \theta \) is the angle of the incline (38.1 degrees).

We can rearrange the formula to solve for \( d \):

\[
d = \frac{W}{F \cdot \cos(\theta)}
\]

### Step-by-step calculation:
1. First, calculate \( \cos(38.1^\circ) \):
   \[
   \cos(38.1^\circ) \approx 0.788
   \]

2. Now, substitute the values into the equation:
   \[
   d = \frac{493.1}{64.9 \cdot 0.788}
   \]
   \[
   d \approx \frac{493.1}{51.14}
   \]
   \[
   d \approx 9.64 \, \text{meters}
   \]

Thus, the man pushed the box approximately **9.6 meters** along the ramp.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would friction on the ramp affect the work done and distance calculated?
2. What if the force was applied parallel to the incline—how would the calculation change?
3. Can we use energy conservation principles to solve similar problems?
4. How does the angle of the incline affect the distance a box is pushed for the same work?
5. How would the calculation differ if the box were being lifted vertically rather than pushed up a ramp?

**Tip:** Always ensure that the angle used in work calculations corresponds to the angle between the force direction and the direction of motion.

A man applies a constant horizontal force of 64.9 N to a box sitting on an incline of 38.1 degrees. If he does 493.1 J of work, how far along the ramp did he push the box?

Learn how to calculate the distance a box is pushed along an incline using a 64.9 N horizontal force and 493.1 J of work on a 38.1-degree incline. This problem involves the work-energy principle and trigonometry concepts, suitable for students in Grades 9-12.

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