Answer
The magnitude of the angular momentum about the origin is $~~12~kg~m^2/s$
Work Step by Step
We can find the magnitude of the angular momentum about the origin:
$L = rmv~sin~\phi$
$L = (3.0~m)(2.0~kg)(4.0~m/s)~sin~(180^{\circ}-\theta_2)$
$L = (3.0~m)(2.0~kg)(4.0~m/s)~sin~150^{\circ}$
$L = 12~kg~m^2/s$
The magnitude of the angular momentum about the origin is $~~12~kg~m^2/s$
