Answer
The original speed of the mess kit is $~~3.5~m/s$
Work Step by Step
We can find the north component of the momentum:
$p_{north} = (2.0~kg)(3.0~m/s)+(2.0~kg)(5.0~m/s)~sin~30^{\circ}$
$p_{north} = 11.0~kg~m/s$
We can find the east component of the momentum:
$p_{east} = (2.0~kg)(5.0~m/s)~cos~30^{\circ}$
$p_{east} = 8.66~kg~m/s$
We can find the magnitude of the momentum:
$p = \sqrt{(11.0~kg~m/s)^2+(8.66~kg~m/s)^2}$
$p = 14.0~kg~m/s$
We can find the original speed:
$m~v = p$
$v = \frac{p}{m}$
$v = \frac{14.0~kg~m/s}{4.0~kg}$
$v = 3.5~m/s$
The original speed of the mess kit is $~~3.5~m/s$
