Answer
The magnitude of the velocity of the third piece is $~~14.1~m/s$
Work Step by Step
We can use conservation of momentum to find the momentum of the third piece in unit-vector form:
$p_1+p_2+p_3 = p_i$
$p_1+p_2+p_3 = 0$
$p_3 = -p_1-p_2$
$p_3 = [-(-30m)~\hat{i}-(-30m)~\hat{j}]~kg~m/s$
$p_3 = (30m~\hat{i}+30m~\hat{j})~kg~m/s$
We can find the velocity of the third piece:
$m~v = p_3$
$m~v = (30m~\hat{i}+30m~\hat{j})~kg~m/s$
$v = \frac{(30m~\hat{i}+30m~\hat{j})~kg~m/s}{3m~kg}$
$v = (10~\hat{i}+10~\hat{j})~m/s$
We can find the magnitude of the velocity:
$v = \sqrt{(10~m/s)^2+(10~m/s)^2}$
$v = 14.1~m/s$
The magnitude of the velocity of the third piece is $~~14.1~m/s$
