C

To find the radius of curvature of the projectile at its highest point, we can use the following step-by-step approach:

**Step 1: Understand the motion and forces**
The projectile motion can be described by its horizontal and vertical components. At the highest point, the vertical component of the velocity becomes 0, and only the horizontal component remains. The velocity at the highest point, $v_x = u imes ext{cos} \theta$.

**Step 2: Determine acceleration**
The only force acting on the projectile is gravity, which accelerates the ball downward with an acceleration of $g$. The acceleration along the vertical direction at the highest point is thus $a = -g$.

**Step 3: Use the formula for radius of curvature**
The radius of curvature $R$ at any point in the trajectory is given by the formula:
$$R = \frac{(v^2)}{a}$$
where $v$ is the velocity at that point and $a$ is the acceleration perpendicular to that velocity.
At the highest point:
- Velocity $v = u \cos \theta$
- Acceleration $a = g$.

**Step 4: Substituting values into the formula**
$$R = \frac{(u \cos \theta)^2}{g}$$

**Step 5: Final answer**
Therefore, the radius of curvature at the point is given by: $R = \frac{u^2 \cos^2 \theta}{g}$. Therefore the correct option is (C).