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The problem describes a pendulum with a bob at the end of a string 4 meters long, where the bob is 25 cm (or 0.25 m) higher at the highest point of its swing than at the lowest point. We need to find the angle of swing, \(\theta\), on each side of the vertical.

We can approach this problem using trigonometry. Here’s the breakdown:

1. **Pendulum Length**: \( L = 4 \, \text{m} \)
2. **Height Difference**: \( h = 0.25 \, \text{m} \)

At the highest point of the swing, the vertical displacement forms a triangle where:
- The pendulum length \(L\) is the hypotenuse,
- The vertical distance from the lowest point to the highest point is \(L - h\),
- The angle \(\theta\) is between the string at the maximum displacement and the vertical.

The vertical component of the pendulum at maximum displacement is \( L \cos(\theta) \), so:
\[
L - h = L \cos(\theta)
\]

Substituting the known values:
\[
4 - 0.25 = 4 \cos(\theta)
\]
\[
3.75 = 4 \cos(\theta)
\]
\[
\cos(\theta) = \frac{3.75}{4} = 0.9375
\]

Now, solve for \(\theta\):
\[
\theta = \cos^{-1}(0.9375)
\]

Let me calculate that angle.The angle of swing on each side of the vertical is approximately \(20.36^\circ\).

Would you like further clarification or details on any part of this solution?

Here are five related questions for deeper exploration:
1. How would the angle change if the length of the pendulum were increased to 5 meters?
2. What would happen to the angle if the height difference were only 10 cm?
3. Can you determine the period of the pendulum’s swing given its length?
4. How is energy conserved in this pendulum system at different points in its motion?
5. How would the result change if the pendulum were swinging in a medium with air resistance?

**Tip:** For problems involving pendulums, understanding the relationship between gravitational potential energy at the highest point and kinetic energy at the lowest point is crucial for analyzing motion.

The bob of a pendulum 4 m long is 25 cm higher at the top of its swing than it is at the bottom. Find the angle of swing on each side of the vertical.

This detailed guide explains how to calculate the angle of swing of a 4-meter-long pendulum, where the bob is 25 cm higher at the top than at the bottom. Learn how to use trigonometric functions such as cosine to solve the problem. Suitable for high school students.

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