A

Step 1: Understand the motion of the particle. When a particle is fired with an initial velocity $u$ at an angle $\theta$ with the horizontal, it has two components of velocity: the horizontal component, $u \cos \theta$, and the vertical component, $u \sin \theta$.

Step 2: Analyze the vertical motion. At the highest point of the projectile's trajectory, the vertical component of the velocity becomes zero, while the horizontal component remains unchanged. Thus, the velocity at the highest point is only the horizontal component:
$V_{highest} = u \cos \theta$.

Step 3: Calculate the change in velocity. The initial velocity of the particle is $u$, with horizontal and vertical components. The change in velocity when the particle reaches its highest point is the difference between the initial velocity and the velocity at the highest point. As the particle has no vertical component at this point, the change in velocity can be considered as the reduction of the vertical component:
Change in velocity at highest point = $V_{initial} - V_{highest} = (u) - (u \cos \theta)$.

Step 4: Examine the relationship. However, we often refer to the horizontal motion when evaluating the effective change in motion, as the vertical component has effectively transformed due to gravitational influence. Therefore, the relevant change in terms of velocity moving forward (at the highest) is $u \cos \theta$, which remains constant horizontally, reaffirming option A as valid.

Therefore, the change in velocity at the highest point is determined primarily by the horizontal component, yielding the result. Hence, the correct answer is Option A: $u \cos \theta$.