A neutron has a kinetic energy such that its initial velocity is \(\mathbf{v}_{i}^{n}=610^{5} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\). It strikes a proton, a particle which can be assumed to have the same mass, initially at rest. It is observed that after the collision the proton moves with a velocity of magnitude \(v_{f}^{p}=4.610^{5} \mathrm{~m} / \mathrm{s}\) at an angle of \(40^{\circ}\) with respect to the direction of incidence of the neutron. Calculate the velocity \(\mathbf{v}_{f}^{n}\) of the neutron after the collision.