A small particle of mass $$m$$ is projected at an angle $$\theta$$ with the x-axis with an initial velocity $$v_0$$ in the $$x-y$$ plane as shown in the figure. At a time $$t < \frac{v_0 \sin\theta}{g}$$, the angular momentum of the particle is where $$\hat{i}, \hat{j}$$ and $$\hat{k}$$ are unit vectors along x, y and z-axis respectively.

A

$$-mgv_0 t^2 \cos\theta \, \hat{j}$$

B

$$mgv_0 t \cos\theta \, \hat{k}$$

C

$$-\frac{1}{2} mgv_0 t^2 \cos\theta \, \hat{k}$$

D

$$\frac{1}{2} mgv_0 t^2 \cos\theta \, \hat{i}$$