A particle is launched horizontally with initial speed \(v_0\) from the top of a cliff of height \(H\) at time \(t = 0\). The particle moves under the influence of constant downward gravitational acceleration of magnitude \(g\). In addition, a horizontal wind exerts a force producing a time-dependent horizontal acceleration \(a_x(t) = -b t\), where \(b\) is a positive constant and the positive \(x\)-direction is aligned with the initial velocity. Which of the following expressions represents the horizontal position \(x\) of the particle when it lands at the base of the cliff (\(y = 0\))?