Sarah is being pushed by Mark with a force of 30 N over a horizontal distance of 25 m as part of a dance performance on a smooth floor. If Mark's push makes a constant angle of 15° with the horizontal, how much work did Mark do on Sarah during the performance?
A. 720 J
B. 725 J
C. 725.5 J
D. 724.7 J


To find the work done by Mark on Sarah, we use the formula for work done when a force is applied at an angle:

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

where:
- \( F = 30 \, \text{N} \) is the force applied,
- \( d = 25 \, \text{m} \) is the distance over which the force is applied,
- \( \theta = 15^\circ \) is the angle between the force and the horizontal direction.

### Step-by-Step Calculation

1. Calculate \( \cos(15^\circ) \):
   \[
   \cos(15^\circ) \approx 0.9659
   \]

2. Substitute values into the work formula:
   \[
   W = 30 \cdot 25 \cdot 0.9659
   \]

3. Perform the multiplication:
   \[
   W \approx 724.425 \, \text{J}
   \]

Rounding to the nearest tenth, we get:
\[
W \approx 724.4 \, \text{J}
\]

### Answer

The closest answer is:
**D. 724.7 J**

Would you like more details or have any questions?

---

1. What is the significance of the angle in calculating work?
2. How does the force direction affect work done if the angle were 90°?
3. Why is work measured in joules?
4. How would friction affect the work calculation?
5. How do we calculate work if the force is not constant?

**Tip:** When calculating work with an angle, always use the horizontal component of the force for accurate results.

Sarah is being pushed by Mark with a force of 30 N over a horizontal distance of 25 m as part of a dance performance on a smooth floor. If Mark's push makes a constant angle of 15° with the horizontal, how much work did Mark do on Sarah during the performance? A. 720 J B. 725 J C. 725.5 J D. 724.7 J

Learn how to calculate the work done when a force of 30 N is applied at a 15° angle over 25 m. This problem covers key physics concepts like work, force, and trigonometry, and is suitable for students in Grades 9-12.

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