A super dart of mass \(20\,\text{g}\), traveling at \(350\,\text{m/s}\), strikes a steel plate at an angle of \(30^\circ\) with the plane of the plate, as shown in the figure. It bounces off the plate at the same angle but at a speed of \(320\,\text{m/s}\). What is the magnitude of the impulse that the plate gives to the bullet?