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conserve momentum. If the incoming particle has velocity v0 i, and leaves with speed v1, then we have
2.8 * v0 i = 2.8 * v1 cos23° i + 2.8 * v1 sin23° j + 5*14 cos39° i - 5*14 sin39° j
equating the i and j parts,
2.8 v0 = 2.577 v1 + 54.4
0 = 1.094 v1 - 44.052
now just solve for v0 and v1