B

To find the radius of curvature (R) at the highest point of projectile motion, we can use the formula for the radius of curvature in terms of speed (v) and acceleration (a) at that point.
Step 1: At the highest point, the vertical component of velocity is zero, and the horizontal component remains constant as v = u cos(θ).
Step 2: The only acceleration acting on the particle at this point is the gravitational acceleration (g), which acts downward. Thus, a = g.
Step 3: The radius of curvature can then be calculated using the formula:
$$R = \frac{v^2}{a}$$ where v is the horizontal velocity and a is the vertical acceleration.
Step 4: Substitute for v and a:
$$R = \frac{(u \cos(θ))^2}{g}$$
Step 5: This expression represents the radius of curvature at the highest point of the projectile's path. Replacing components as needed will help you determine the exact numerical value based on variable inputs.
Therefore, the radius of curvature at the highest point is provided in option B.