A golf ball of mass \(m\) is initially at rest on a horizontal tee. A golf club strikes the ball, exerting a horizontal force on it. The magnitude of the force exerted by the club on the ball as a function of time \(t\) is modeled by the equation \(F(t) = C t (t_f - t)\), where \(C\) is a positive constant and \(t_f\) is the total time the club is in contact with the ball. The collision begins at \(t = 0\).