Let two particles (m1 = m2 = 1 kg) repel each other with equal and opposite forces given b...

Let two particles (m1 = m2 = 1 kg) repel each other with equal and opposite forces given by

where b = 1 in and k = 1 N. Assume that the initial positions of m1 and m2 are given by (x1, y1)0 = (−10, 0.5) m and (x2, y2)0 = (0. −0.5) m. Let the initial velocity of m1 be 10 m/s in the +x direction and m2 be at rest. Numerically integrate the equations of motion for these two particles undergoing this two-dimensional “collision.”

(a) Plot their trajectories up to a point where their distance of separation is 10 m.

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(b) Measure the scattering angle of the incident particle and the recoil angle of the scattered particle. Is the sum of these two angles equal to 90°?

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(c) What is the vector sum of their final momenta? Is it equal to the initial momentum of the incident particle?