Consider a pendulum consisting of a massless string with a mass at one end. The mass is held with the string horizontal and then released. The mass swings down, and on its way back up, the string is cut at point P when it makes an angle of with `theta` the vertical. Find the angle for `theta` which horizontal range .R. is maximum.

Explanation

To solve the problem of finding the angle \( \theta \) for which the horizontal range \( R \) is maximum when the pendulum's string is cut, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
The pendulum consists of a mass attached to a massless string. When the mass is released from the horizontal position, it swings down and gains speed due to gravitational potential energy converting into kinetic energy.

2. **Applying Conservation of Energy**:
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