A small stone is fastened to the top of a standard cart of inertia \(1 \mathrm{~kg}\) to form a combination of unknown inertia \(m_{1}\). A second standard cart is then launched with an initial velocity given by \(v_{s x, i}=+0.46 \mathrm{~m} / \mathrm{s}\) toward the combination that is initially at rest. After the collision, the \(x\) component of the velocity of the cart with the stone is \(v_{\mathrm{ux}, \mathrm{f}}=+0.38 \mathrm{~m} / \mathrm{s}\) and that of the standard cart is \(v_{\mathrm{s} x, \mathrm{f}}=-0.08 \mathrm{~m} / \mathrm{s}\). What is the inertia of the stone?