In Ancient Greece, athletes competing in the long jump used handheld weights called halteres to lengthen their jumps. You are a 78 kg history major on the track and field team and decide to try this strategy. You jump at 10.3 m/s, 22.8 degrees above the horizontal. At the peak of your jump you throw two 5.5 kg masses horizontally behind you such that their velocity is zero in the ground's reference frame. What distance do the halteres add to the jump in m?