A \(2.0 \text{ kg}\) cart is moving with an unknown speed \(v_0\) on a horizontal, frictionless table. It collides with and sticks to a second \(2.0 \text{ kg}\) cart that is initially at rest. The combined carts then slide off the edge of the table, which is \(5.0 \text{ m}\) above the floor, and land a horizontal distance of \(4.0 \text{ m}\) from the base of the table. What is the initial speed \(v_0\) of the first cart? (Use \(g = 10 \text{ m/s}^2\))