Answer
The final momentum vector P is the sum of the two initial momentum vectors, each with amount of momentum p.
In terms of magnitude, $P=1.41p$.
Work Step by Step
The incoming momentum vectors are perpendicular. Use the Pythagorean theorem to find the magnitude of the combined momentum.
$$p^{2}+p^{2}=P^{2}$$
$$P=1.41p$$
