A particle of mass `m` is projected with a speed `u` at an angle `theta` to the horizontal at time `t = 0`. Find its angular momentum about the point of projection `O` at time `t`, vectorially. Assume the horizontal and vertical lines through `O` as `X` and `Y` axes, respectively.

Explanation

To find the angular momentum of a particle of mass `m` projected with an initial speed `u` at an angle `theta` to the horizontal at time `t`, we will follow these steps:

### Step 1: Determine the position vector of the particle at time `t`
The position of the particle at time `t` can be described using the horizontal and vertical components of the motion.

- The horizontal displacement \( x \) is given by:
\[
x = u \cos(\theta) t
...