Particles are scattered classically by a potential: V (r) = U(1 − r 2/a2 ), for r ≤ a 0, for r > a , U is a constant. Assume that U > 0. A particle of mass m is coming in from the left with initial velocity v0 and impact parameter b < a. Hint: work in coordinates (x, y) not (r, φ). 1. What are the equations of motion for determining the trajectory x(t) and y(t) when r < a? 2. Assume that at t = 0 the particle is at the boundary of the potential r = a. Solve your equations from the previous part to find the trajectory x(t) and y(t) for the time period when r < a. Express your answer in terms of sinh and cosh functions. 3. For initial energy 1 2mv2 0 = U, find the scattering angle θ as function of b.