A $2.0 kg$ object moves in a plane with velocity components $v_x=30 m/s$ and $v_y= 60 m/s$ as it passes through the point $(x, y) = (3.0, -4.0)m$. What is its angular momentum relative to the point $(-2.0,-2.0)m$ at the same moment.

$$\begin{gathered} Given, \overrightarrow{v}=\left(30\hat{i}+60\hat{j}\right) m/s \\ \overrightarrow{r}=\left(3\overrightarrow{i}-4\overrightarrow{j}\right) m \\ Here \overrightarrow{r}=\left[\left(3-\left(-2\right)\overrightarrow{i}-4-\left(-2\right)\overrightarrow{j}\right) \right] \\ =\left(5\overrightarrow{i}-2\overrightarrow{j}\right) m \\ The angular mometum, \\ \overrightarrow{L}=m\left(\stackrel{\rightharpoonup }{r}\times \overrightarrow{v}\right) \\ =2\left[\left(5\overrightarrow{i}-2\hat{j}\right)\times \left(30\hat{i}+60\hat{j}\right)\right] \\ = 720 \hat{k} kg-m^2/s \end{gathered}$$