Answer
The magnitude of the momentum of the daughter nucleus is $~~1.36\times 10^{-22}~kg~m/s$
Work Step by Step
Note that the initial momentum is 0.
We can use conservation of momentum to find the momentum $p_n$ of the daughter nucleus:
$p_f = p_i$
$p_n+(-1.2\times 10^{-22}~kg~m/s)~\hat{i}+(-6.4\times 10^{-23}~kg~m/s)~\hat{j} = 0$
$p_n = (1.2\times 10^{-22}~kg~m/s)~\hat{i}+(6.4\times 10^{-23}~kg~m/s)~\hat{j}$
We can find the magnitude of the momentum of the daughter nucleus:
$p_n = \sqrt{(1.2\times 10^{-22}~kg~m/s)^2+(6.4\times 10^{-23}~kg~m/s)^2}$
$p_n = 1.36\times 10^{-22}~kg~m/s$
The magnitude of the momentum of the daughter nucleus is $~~1.36\times 10^{-22}~kg~m/s$
