A particle of mass `m` has been thrown with intial speed `u` making angle `theta` with the horizontal ground. Find the angular momentum of the projectile about an axis perpendicular to the plane and passing through the point of projection when the projectile is
`(a)` At the highest point
`(b)` About to hit the ground

Explanation

To find the angular momentum of a projectile about an axis perpendicular to the plane and passing through the point of projection, we will solve the problem in two parts: (a) when the projectile is at its highest point and (b) when it is about to hit the ground.

### Part (a): Angular Momentum at the Highest Point

1. **Identify the velocity at the highest point**:
At the highest point of its trajectory, the vertical component of the velocity becomes zero. The horizontal component remains:
\[
v_x = u \cos \theta
...