By accident, a large plate is dropped and breaks into three pieces. Three pieces with masses m1, m2, and m3, fly apart parallel to the floor: piece 1 has velocity V1 = 7 m/s and angle θ1 = 36° with respect to the positive y-axis, piece 2 has velocity V2 = 5 m/s and angle θ2 = 57° with respect to the positive x-axis, and piece 3 has velocity V3 = 3 m/s, mass m3 = 1.6 kg, and making an angle θ3 = 0 with respect to the negative y-axis (see the drawing below). As the plate falls, its momentum has only a vertical component, and no component parallel to the floor. After the collision, and using the fact that the component of the total momentum parallel to the floor must remain zero (because the net external force acting on the plate has no component parallel to the floor), then find the mass of piece #1: m1 [in grams].