What is the relevant equation if object is at origin and velocity is $$v_0=i+j$$​ ?

Correct option is B

​$$\textbf{Given:} \\\quad \bullet\ \text{Initial velocity: } \vec{v}_0 = \hat{i} + \hat{j} \\\quad \bullet\ \text{Object starts from origin: } \vec{r}_0 = 0 \\\quad \bullet\ \text{Acceleration in vertical direction (assuming projectile motion): } a_y = -g = -10\, \text{m/s}^2 \\\\\text{In projectile motion with an initial velocity of } \hat{i} + \hat{j}, \text{ we can resolve the velocity and use the equations of motion:} \\\text{For horizontal motion:} \quad x(t) = v_{0x} t = t \\\text{For vertical motion:} \quad y(t) = v_{0y} t - \frac{1}{2} g t^2 = t - 5t^2 \\\\\textbf{Solution:} \\\text{We write the position vector } \vec{r}(t) \text{ as:} \\\quad \vec{r}(t) = \hat{i} \cdot x(t) + \hat{j} \cdot y(t) \\\quad \vec{r}(t) = \hat{i}(t) + \hat{j}(t - 5t^2)$$​​