An aerial fireworks shell is momentarily at rest at the highest point of its trajectory when it explodes into exactly three fragments. Immediately after the explosion, a \(0.50 \text{ kg}\) fragment travels due east along the \(+x\)-axis at \(24 \text{ m/s}\), and a \(1.0 \text{ kg}\) fragment travels due north along the \(+y\)-axis at \(16 \text{ m/s}\). If the third fragment has a mass of \(0.80 \text{ kg}\), what is the speed of the third fragment immediately after the explosion?