C

When a particle is thrown horizontally, its motion can be analyzed in two components: horizontal and vertical.
1. **Vertical Motion**: The particle experiences free fall under gravity, with the vertical displacement given by:
$$y = \frac{1}{2}gt^2$$
where g is the acceleration due to gravity and t is the time. The vertical velocity at time t is given by:
$$v_y = gt$$

2. **Horizontal Motion**: The horizontal velocity remains constant (initial horizontal velocity u).

3. **Resultant Velocity**: The resultant velocity V at time t can be found using Pythagoras' theorem, considering both the horizontal and vertical components:
$$V = \sqrt{u^2 + (gt)^2}$$
This matches with option C.
Therefore, the correct answer is C.