If the initial velocity in the horizontal direction of a projectile is represented by the unit vector $$\hat{i}$$ and the equation of the trajectory is given by $$y = 5x(1 - x)$$, we need to find the $$y$$ component vector of the initial velocity. (Given: $$g = 10 \mathrm{\ m/s^2}$$)

The trajectory equation can be expanded as:

$$y = 5x - 5x^2$$

In the general form of a projectile's trajectory: $$y = x \tan \theta - \frac{1}{2} \frac{g x^2}{v_0^2}$$

Here, the equation compares as follows:

$$\tan \theta = 5 = \frac{u_y}{u_x}$$

Given that the initial horizontal velocity component, $$u_x$$, is 1 (unit vector $$\hat{i}$$), we can find $$u_y$$ from the relationship:

$$u_y = 5 \times 1 = 5$$

Therefore, the $$y$$ component vector of the initial velocity is 5$$\hat{j}$$.